victor lopes takahashi wireless ultrasonic energy and data
TRANSCRIPT
Victor Lopes Takahashi
Wireless ultrasonic energy and data transmission through fluid and metallic layers
Dissertação de Mestrado
Dissertation presented to the programa de Pós-graduação em engenharia mecânica of PUC-Rio in partial fulfillment of the requirements for the degree of Mestre em Engenharia Mecânica.
Advisor: Prof. Arthur Martins Barbosa Braga
Co-Advisor: Prof. Alan Conci Kubrusly
Rio de Janeiro October 2017
Victor Lopes Takahashi
Wireless ultrasonic energy and data transmission through fluid and metallic layers
Dissertation presented to the programa de Pós-graduação em engenharia mecânica of PUC-Rio in partial fulfillment of the requirements for the degree of Mestre em Engenharia Mecânica. Approved by the undersigned Examination Committee:
Prof. Arthur Martins Barbosa Braga Advisor
Departamento de Engenharia Mecânica – PUC-Rio
Prof. Alan Conci Kubrusly Co-Advisor
Centro de Estudos em Telecomunicações – PUC-Rio
Prof. Julio Cezar Adamowski Departamento de Engenharia Mecatrônica e de Sist. Mecânicos – USP
Dr. Miguel de Andrade Freitas
Centro de Pesquisa em Tecnologia de Inspeção – PUC-Rio
Prof. Márcio da Silveira Carvalho Vice Dean of Graduate Studies
Centro Técnico Científico – PUC-Rio
Rio de Janeiro, October 11th, 2017
All rights reserved.
Victor Lopes Takahashi
The author graduated in Electrical Engineering from PUC-Rio in 2014. Currently works in the Laboratório de Sensores à Fibra Óptica as Research Engineer.
Bibliographic data
CCD: 621
Takahashi, Victor Lopes
Wireless ultrasonic energy and data transmission through
fluid and metallic layers / Victor Lopes Takahashi ; advisor: Arthur
Martins Barbosa Braga ; co-advisor: Alan Conci Kubrusly. – 2017.
117 f. : il. color. ; 30 cm
Dissertação (mestrado)–Pontifícia Universidade Católica
do Rio de Janeiro, Departamento de Engenharia Mecânica, 2017.
Inclui bibliografia
1. Engenharia Mecânica – Teses. 2. Ondas
ultrassônicas. 3. Comunicação por ultrassom. 4. Modelo analítico.
5. Modelo elétrico. I. Braga, Arthur Martins Barbosa. II. Kubrusly ,
Alan Conci. III. Pontifícia Universidade Católica do Rio de Janeiro.
Departamento de Engenharia Mecânica. IV. Título.
Aos meus pais, Ana Beatriz e George, pela
entrega e dedicação.
Acknowledgment
I would like to dedicate this work to my parents for the commitment and
dedication throughout life.
To my sister, Ivana, for the eternal partnership and friendship.
To my advisor, Arthur Braga, for the professional and academic support, also for
the past ten years of conviviality at the Optic Fiber Sensor Laboratory.
To my co-advisor, Alan Kubrusly, for the patience, dexterity and extreme wisdom
conducting his academic insights.
To my friend, Sully Quintero, for the full dedication as a professional and for the
great fellowship in life practice.
To my partner in life, Ana Luiza, for her positive energy and to show me the way
to my own self-knowledge.
To my friend, Sávio Weslley, for the many hours of intense academic debating,
for the support to my academic activities and also for his friendliness.
To PUC-Rio for the aid granted, which I could not accomplish this work without.
Abstract
Takahashi, Victor Lopes; Braga, Arthur Martins Barbosa (Adviser);
Kubrusly, Alan Conci (Co-adviser). Wireless ultrasonic energy and data
transmission through fluid and metallic layers. Rio de Janeiro, 2017.
117p. Dissertação de Mestrado – Departamento de Engenharia Mecânica,
Pontifícia Universidade Católica do Rio de Janeiro.
Nonintrusive power transfer and data communication between devices
through metallic walls is an increasing need in several sensing systems. Traditional
means of communication mainly use electric conductors or electromagnetic waves.
The first needs some mechanism for penetration whereas the latter, although
nonintrusive, can be extremely limited due to the Faraday shielding effect. An
alternative is found in the use of acoustic waves to transfer data and energy through
metallic walls. Although great effort has been recently directed towards this type of
communication, there still is a shortage of data dealing with the acoustic channel in
the presence of multiple layers as well as of experimental results with curved
metallic walls. Possible applications in these contexts may be found when
monitoring pressure vessels filled with a fluid or pipes conveying liquids. The
present dissertation evaluates, analytically, numerically and experimentally, the
transmission of energy and data communication through a multi-layered, liquid-
metal acoustic channel, composed of two curved metallic walls with a layer of
liquid between them. For this, initially, two models based on propagation of
ultrasonic waves are analyzed and compared, one analytical and the other
numerical, both relying on electric-acoustic analogies. Both are extended to include
more than one layer of material. The energy efficiency assessment and data transfer
capability are addressed through the models and also experimentally validated
using an acoustic channel comprising a flat aluminum plate and two axially aligned
piezoelectric transducers coupled to it. In addition, an electric circuit is developed
for the transmission of energy from outside to inside and the communication of
digital data from the inside to the outside by ASK modulation and demodulation.
The circuit is simulated using electrical circuit simulation software, designed and
assembled with printed circuit boards. Thereafter, a second experiment where the
acoustic channel is composed by a curved metallic section with an intermediate
fluid layer is implemented. In this, the power and data transfer are studied using the
developed electric circuit, which is connected to a pair of piezoelectric transducers
coupled to the acoustic channel. Results for the flat aluminum plate reveal good
agreement between both models and the experiment, both by frequency and time
domain analysis. The analytical model best reproduced the physical phenomenon
of interest due to its stricter treatment of loss mechanisms. The second experiment
proved the feasibility of multi-layered liquid-metal communication on curved walls
and showed that the system is able to transmit data from temperature and pressure
sensors at a rate of 9600 bps. The sensor and all its peripheral circuitry were fully
powered by the energy flowing through the acoustic channel in total of
approximately 140 mW.
Keywords Ultrasonic waves; Ultrasonic communication; Analytic model; Electric
model.
Resumo
Takahashi, Victor Lopes; Braga, Arthur Martins Barbosa; Kubrusly, Alan
Conci. Comunicação sem fio e transferência de energia através de
paredes metálicas e camada de líquido utilizando ondas ultrassônicas.
Rio de Janeiro, 2017. 117p. Dissertação de Mestrado – Departamento de
Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro.
Existe uma crescente necessidade em transferir energia e comunicar dados
entre dispositivos através de paredes metálicas de forma não intrusiva . Os meios
de comunicação tradicionais para este fim, em sua maioria, baseiam-se
essencialmente no uso de condutores elétricos ou ondas eletromagnéticas. O
primeiro necessita de algum mecanismo de penetração e o segundo, apesar de não
intrusivo, torna-se limitado devido ao efeito de blindagem de Faraday. Uma
alternativa é encontrada no uso de ondas acústicas para transferir os dados e energia
através de paredes metálicas. Recentemente, grande esforço tem sido empregado
nesse tipo de comunicação, todavia há ainda carência de trabalhos que tratem do
canal acústico na presença de multicamadas além de resultados experimentais com
paredes metálicas curvas. Possíveis aplicações nestes contextos são encontrados no
monitoramento de vasos de pressão com fluido no seu interior ou até mesmo de
tubulações metálicas transportando líquidos. A presente dissertação avalia, de
forma analítica, numérica e experimental, a transmissão de energia e a comunicação
através de um canal acústico composto por camadas metal-líquido-metal com
paredes curvilíneas. Para tal, inicialmente, são analisados e comparados dois
modelos, existentes na literatura, fundamentados na propagação de ondas
ultrassônicas, um analítico e outro numérico, ambos baseados em analogias
acustoelétricas. Os dois modelos são estendidos permitindo a inclusão de múltiplas
camadas de diferentes materiais. A avaliação da eficiência de energia e a capacidade
de transferência de dados é feita com base nos modelos e validada
experimentalmente utilizando uma placa reta de alumínio e um par de transdutores
piezoelétricos axialmente alinhados e acoplados ao mesmo. Um circuito elétrico é
desenvolvido para a transmissão de energia entre as duas faces da placa e para a
comunicação de dados digitais por meio de modulação do tipo ASK. O circuito é
então simulado utilizando-se um software de simulação de circuitos elétricos,
projetado e montado com placas de circuito impresso. Em seguida, é realizado um
segundo experimento utilizando uma seção curva metálica com uma camada
intermediária de água como canal acústico . Nesse, são estudadas as transferências
de energia e dados utilizando o circuito elétrico desenvolvido o qual é conectado a
um par de transdutores piezoelétricos acoplados ao canal acústico. Resultados do
experimento na placa reta de alumínio revelam boa consonância entre os modelos
e o experimento, tanto por uma análise em frequência quanto no domínio do tempo.
Tendo sido o modelo analítico o que melhor representa o fenômeno físico em
questão devido ao maior rigor no tratamento do mecanismo de perdas. Para o
segundo experimento, resultados comprovam a possibilidade de comunicação
através de múltiplas camadas metálicas e líquidas em paredes curvas, mostrando
que o sistema é capaz de transmitir dados de um sensor de temperatura e pressão a
uma taxa de 9600 bps. Tanto o sensor quanto os seus circuitos periféricos são
integralmente alimentados pela energia que atravessa o canal acústico, num total de
aproximadamente 140 mW.
Palavras-chave Ondas ultrassônicas; Comunicação por ultrassom; Modelo analítico; Modelo
elétrico
Table of Contents
1 Introduction 15
1.1 Objective 18
1.2 Dissertation contribution 18
1.3 Dissertation layout 19
2 Bibliography review 21
3 Analytical and numerical design 35
3.1 Pspice modeling 35 3.1.1 Piezoelectric transducer model 35 3.1.2 Intermediate layer model 41 3.1.3 Pspice loss considerations 44 3.1.4 Full system model 47 3.1.5 Analysis of power transfer 49 3.1.6 Analysis of data communication 50 3.2 Analytical modeling 51 3.2.1 Two-port ABCD matrix 52 3.2.2 Piezoelectric transducer model 53 3.2.3 Intermediate layer 56 3.2.4 Analytical loss considerations 58 3.2.5 Analysis of power transfer 61 3.2.6 Analysis of data communication 62 3.3 Models verification and comparison 64
4 PDAC implementation 70
4.1 ASK 70
4.2 Outside block circuit 71
4.3 Inside block circuit 74
4.4 Full system simulations 76
4.5 Full system simulation results 76
4.5.1Outside block simulation 78
4.5.2 Inside block simulation 79
4.6 Experimental setup 81 4.6.1 Flat plate 82 4.6.1.1 Flat plate power 84 4.6.1.2 Flat plate communication analysis 86 4.6.2 Curved surface - Tube 90 4.6.2.1 Curved surface power transfer analysis 93 4.6.2.2 Curved surface data communication analysis 94 4.6.3 Full system experimental analysis - Tube 97
5 Conclusion 104
6 Bibliographic reference 107
Figure list
Figure 1.1 “sandwiched” PZT transducers between a metal layer, redrawn from [63] 16
Figure 1.2 Diagram of power and data communication through acoustic channel. Power is provided from the outside block to the inside block whereas sensor information is transmitted from the inside block to the outside block. 17
Figure 1.3 a) Flat plate with the PZT transducers (red rectangles) co-aligned b) Curved surface in the presence of water 18
Figure 2.1 Diagram developed by Imoru et al. [19] to evaluate the power transfer through a metal pipe. Reproduced from [19]. 22
Figure 2.2 A pipe made of stainless steel with an internal coil and an external coil that entirely enclose the pipe, redrawn from [20] 22
Figure 2.3 Basic configuration of a capacitive power transfer, redrawn from [22] 23
Figure 2.4 Configuration of 2 PZT transducers co-aligned an attached to the metal wall, redrawn from [67] 25
Figure 2.5 (a) Single-hop (b) Double-hop and (c) reflected-power configuration, redrawn from [43] 28
Figure 2.6 Power and data communication of a sensor inside metallic envelope, redrawn from [53] 30
Figure 3.1 Overall diagram of PDAC generic system 34
Figure 3.2 Diagram of the piezoelectric transducer 36
Figure 3.3 (a) Transmission line representing the mechanical part controlled by the current (i) and (b) the electrical part of the transducer controlled by the particle velocity 39
Figure 3.4 Transducer subcircuit schematic in ORCAD software 39
Figure 3.5 Spreading attenuation of acoustic wave 46
Figure 3.6 Full system circuit designed in ORCAD 47
Figure 3.7 Acoustic channel with S11 and S21 blocks represented in blue and red, respectively 49
Figure 3.8 Two-port configuration of S-parameters 49
Figure 3.9 Modulation block 51
Figure 3.10 Piezoelectric mechanical and electrical ports, redrawn from [63] 53
Figure 3.11 Equivalent impedance diagram 63
Figure 3.12 Power transfer analysis of both models varying the metal thickness 65
Figure 3.13 Power transfer analysis varying the adhesive thickness 66
Figure 3.14 Input voltage V11 Pspice and analytical 67
Figure 3.15 V11 difference Pspice and analytical 67
Figure 3.16 Output PZT voltage at 2.256 MHz 68
Figure 3.17 Output PZT voltage at 2.235 MHz 68
Figure 4.1 ASK modulation diagram 71
Figure 4.2 Envelope detector schematic 72
Figure 4.3 Envelope Signal and Modulated signal example 72
Figure 4.4 Voltage comparator diagram 73
Figure 4.5 input and output signals of the voltage comparator 74
Figure 4.6 Voltage doubler topology 75
Figure 4.7 Mosfet switching RF carrier 76
Figure 4.8 PDAC full system with electronic peripherals circuits 77
Figure 4.9 Modulated signal of full system 78
Figure 4.10 Sensor signal of full system 78
Figure 4.11 Comparision between sensor information and comparator signal 79
Figure 4.12 Inside PZT signal 80
Figure 4.13 5V voltage regulator output 81
Figure 4.14 Impedance curve for Pspice, Analytical and experimental 85
Figure 4.15 Schematic (a) and experimental (b) characterization of the flat plate using VNA 85
Figure 4.16 Flat plate power analysis 86
Figure 4.17 Setup for data communication analysis in frequency domain 87
Figure 4.18 Voltage divider theory 87
Figure 4.19 (a) Input voltage (V11) varying the termination load and zoom (b) between 2.1 and 2.5 MHz 88
Figure 4.20 Difference in amplitude voltage 88
Figure 4.21 Setup to measure the input voltage (V11) 89
Figure 4.22 Input voltage signal flat plate experimental test 90
Figure 4.23 Three-dimensional sketch of curved surface experiment 92
Figure 4.24 3D CAD and Structure made on 3D printer to isolate the back face of transducer from water 93
Figure 4.25 Power transfer analysis for curved surface experiment 93
Figure 4.26 Input voltage (V11) – curved surface 94
Figure 4.27 Input voltage between 0.95MHz and 1.05MHz – curved surface 95
Figure 4.28 Input voltage difference between 50 and 0.22 ohms, full frequency range 96
Figure 4.29 Input voltage zoom for frequencies between 1 MHz and 1.05 MHz 96
Figure 4.30 Input voltage transient analysis - Curved surface 97
Figure 4.31 Schematic diagram of the curved surface experiment test 98
Figure 4.32 Full system experimental bench 99
Figure 4.33 Sensor information signal in green and the input voltage signal on the outside block in purple 100
Figure 4.34 Block diagram of protocols used in the inside block 101
Figure 4.35 Sensor information signal in green and purple the signal after the voltage comparator in purple 101
Figure 4.36 Comparison between raw and demodulated temperature sensor data 102
Figure 4.37 Bubbles generated inside the water due to cavitation-like phenomenon 103
Table list
Table 3.1 characteristic impedances of common materials 41
Table 3.2 Analogies between mechanical and electrical of PZT transducer 43
Table 3.3 Analogies between mechanical and electrical of intermediate layers 44
Table 3.4 Materials properties 48
Table 3.5 2-port S-parameters 50
Table 4.1 Material properties 84
Table 4.2 Power Transfer of Pspice, analytical and experimental 86
Table 4.3 Highest difference in amplitude 89
Table 4.4 Material properties - Tube 91
Table 4.5 Power transfer peak of curved surface experimental setup 94
Table 4.6 Voltage difference of the input voltage 95
Table 4.7 Power consumption of the main elements
in the inside block 100
1 Introduction
Wireless communications play a key role in integrating a sensor network.
Some communication protocols have become quite popular in recent decades such
as Wi-Fi, Bluetooth, 3G, 4G, among others [1]. All of these protocols, however, use
electromagnetic waves in order to communicate and in some applications, such as
in the presence of metal walls, for instance, the performance of the communication
suffers a great decline mainly because of the Faraday shield phenomenon [2]. As
an alternative, acoustic waves use the material medium to propagate mechanical
waves by oscillating stress/strain field inside the material [3]. Typical applications
where an enclosure metal is present is at ship containers [4], submarines [5] in
hazardous environment [6,18], or even on a wellbore casing, exposed to high
pressure and temperature in which sensors are interrogate through the wellbore wall
[89]. A common scenario consists of sensors located outside the hull of a submarine
or inside the container; these sensors need to send data through the metal wall,
which cannot be penetrated [5]. The sensor maintenance and the associated
peripherals circuits are often very laborious or unfeasible, relying on remote
wireless powering system can be of interest to avoid replacing batteries or power
supplies. Recently, great attention has been drawn by research groups from over the
globe to system which combine data communication and power transmission by
means of acoustic waves [4-10].
The most typical appl ication relies on the configuration of two sandwich-structured
PZT transducers between a metal layer attached to the wall with epoxy or other
acoustic couplant as shown in Fig. 1.1. Using this configuration, results from
literature shows power efficiency varying from 30% to 88% [5-7,12-15] wi th the
thickness of the metal barrier wal l going from 1.6mm to 63.5mm. When speaking
on the data transfer capabili ty, several data transmission protocols were
implemented, for instance FSK[4], ASK[6, 7, 14], OFDM[5,16], QPSK[15]. Data
rate varies dramatical ly from lower 1kbps up to 17.37Mbps, using OFDM.
Despite this, few works implemented a complete system integrat ing sensors and
hardware design [14]; it is also not common to find works report ing analysis of
power and data transfer with multiple layers, especially including a fluid layer. [17]
16
Figure 1.1 sandwich-structured PZT transducers between a metal layer, redrawn from
[63]
The overall system to power and data communication through acoustic channel,
(PDAC) typically contains three major blocks: the “outside block”, “inside block”
and the “acoustic channel”. T hese definitions were primary presented by Prada in
[7] and maintained in this dissertat ion. The “outside block” encompasses the
peripherals ci rcuitry and accessories to create the carrier wave that drives the system
and to demodulate the data information from the sensors, connected to the inside
block. The “inside block” works passively and powers the sensors using exclusively
the energy received from the “outside block”. T he communication of the sensors is
performed modulating the carrier wave generated in the “outside block”. Finally,
the “acoustic channel block” consists on the material medium (which can be
composed by many layers, such as metals, water, and adhesive) and two PZT
transducer. Fig. 1.2 i llustrates the block diagram of the system described. This
configuration has the advantage of been simple to implement and capable of
communicating with baud rates which can reach moderated speeds; the power
received in the “inside block” is sufficient to power sensors and peripheral
electronics with low consumption [14]. Addit ional ly this design allows the inside
block to be inaccessible and to work indefinitely since its power is suppl ied from
outside and ideally it needs no external intervention.
17
Figure 1.2 Diagram of power and data communication through acoustic channel . Power is
provided from the outside block to the inside block whereas sensor information is
transmitted from the inside block to the outside block.
In this dissertation a system which uses the acoustic waves to power and
communicate sensors is investigated by means of numerical model and
experiments. Two models are described and compared, one analytical and other
numerical based on electric circuit simulation software. These two models aid in
evaluating the power t ransfer efficiency between the PZT transducers and data
communication capabi lity of the system. Furthermore, experimental tests were
performed to compare and val idate the results of the models and evaluate the
designed hardware.
Two different setups were evaluated here. The first consist s of a metal flat
plate with two PZT transducers attached by an epoxy glue and geometrically co-
aligned, Fig 1.3 (a); the other is a curved surface with the two PZT transducers also
co-aligned and in the presence of water, Fig. 1.3 (b). T he former, above al l, was
implemented to validate the concept of the PDAC and the latter, concedes the
evaluation of a full system in such applications that include a fluid layer and a
curved surface. The curved configuration is of interest because it could be any
vessel or concentric pipes immersed in water, in which sensors located inside the
inner tube or outside the outer one are not accessible. Thus, this last configuration
can be of potential interest in practical moni toring systems.
18
Figure 1.3 a) Flat plate with the PZT transducers (red rectangles) co -aligned b) Curved surface in the presence of water
The two setups of figure 1.3 were evaluated by the analytical and numerical
models and the results compared with each other and with an experimental setup.
Finally, the full system connecting one pressure and temperature sensor,
communicating and powering through water layer under a curved steel surface was
successfully tested in laboratory conditions.
1.1 Objectives
The main goal of this dissertation is to design and create a system that powers
and communicates a sensor located in the inside block by means of acoustic waves,
in which the acoustic channel is composed by multiple fluid and solid curved layers.
Specific objectives are to evaluate and extend two pre-existing models, including
multilayer, and to assess a comparison between them and experiments.
1.2 Dissertation contribution
This dissertation provides the fol lowing contribution to the existing l iterature:
• Comparison of analyt ical and numerical models between them and between
experiments for a single and multi -layer wi th fluid, by previous extending
the models to include mult iple layers as the acoust ic channel .
19
• Simulation, design and evaluation of the PDAC peripherals ci rcuits
integrated to a sensing system through curved surface in presence of water
layer.
As a bottom line, this is the first work regarding power and data
communication using acoustic waves for the research group, allowing the use of
this research theme and mainly these results to build a framework for further works.
1.3 Dissertation layout The dissertation is organized as follows:
1. Introduction:
Introduces the work.
2. Bibl iography review:
Presents a bibliography review and state of the art for methods to wireless
transmit power and data through metal layers. The review is focused in acoustic
waves’ solutions but also presented electromagnet ic approaches for a complete
understanding of the problem.
3. Analytical and numerical design:
This chapter outl ines the overall system proposed for the PDAC. A
numerical model based on Pspice and an anal yt ical formulation is revisited to
describe the PZT transducer and intermediate layers and their associated losses.
Simulation results in frequency and time domain and a comparison of both models
with a briefly discussion are presented.
4. PDAC implementation:
This chapter presents the discussion about the modulat ion used and a
detailed descript ion about the outside and inside circuit blocks. A full system with
the outside, inside and acoustic channel blocks are simulated in Pspice and the
results discussed. The circuits of inside and outside block, which were designed and
mounted in printed circuit boards, are presented. T hey are responsible to modulate
and demodulated the sensors data and power the inside block. Two experiments are
presented, the first with the flat plate and the other with the curved surface in
20
presence of a fluid. The latter was also used in a full pressure and temperature
sensing system.
5. Discussion and Future Work:
Conclusion with a final discussion of the overall system and a brief out line for future work.
2 Bibliography review
Methods to wireless transmit power and data through a channel can be split
in two major blocks; based on electromagnetic waves and acoustic waves. Although
the main objective of this dissertation is related with acoustic waves an overview
on methods to transmit power and data wirelessly including electromagnetic waves
is essential to outline and compare the crucial points of operation. In this survey,
however, not all the publications specifically concern transmission of power and
data simultaneously.
2.1 Wireless power and data transmission based on electromagnetic waves
Regarding electromagnetic waves some publications stand out. In the first,
Imoru at al. [19] use the principle of inductive coupling to transfer power through
metal. This principle is similar to the coupling of transformers. In a transformer, the
energy is transferred from one coil to another. The primary coil produces an
alternative magnetic field that induces a current on the secondary coil by the
principle of electromagnetic induction. The configuration developed by [19] is
represented in figure 2.1, in which two coils are winded around a pipe section, one
inside and other outside. The outer coil transfer power to the inner one, by inducing
a current in the latter which passes through a resistor. In this publication the author
reports a maximum efficiency of 23% with a load of 5.55Ω operating at 100 Hz in
32.5mm of distance between the radius of each coil.
22
Figure 2.1 Diagram developed by Imoru et al. [19] to evaluate the power transfer through
a metal pipe. Reproduced from [19].
This solution can even transmit data, however with extremely low data
communication, at about 10 bps.
Zangl et al. [20-21], designed an experiment consisting of a steel pipe with
an internal coil connected to a capacitive sensor and an external coil that can entirely
enclose the pipe in order to maximize the power transfer efficiency, see Fig. 2.2.
With 2mm of pipe wall thickness the magnetic flux density decrease 15dB. At 50Hz
the system achieve 20dB of signal to noise ratio when applying 540mA on the
external coil. The author also commented the feasibility to transmit data at more
than 20 kbps.
Figure 2.2 A pipe made of stainless steel with an internal coil and an external coil that
entirely enclose the pipe, redrawn from [20]
23
Other type of configuration to transfer power is the use of electric field instead
of magnetic field, which is established by means of capacitive coupling. Unlike the
inductive coupling which is based on magnetic field coupling to transfer power, the
capacitive coupling uses the electric field coupling. The configuration of a typical
capacitive coupling has two pairs of plates in which an AC voltage is applied. When
two separated pair of plates are placed close to the primary pair, electric fields are
formed. In between these two pairs of plates a metal wall can be applied. Liu and
Chao [22] presented this configuration where the coupling distance of each pair
was 1mm, see Fig. 2.3. The input power was set to 28.8W while the output power
had a decrease down to 12.3W, i.e. achieving 42.7% of efficiency.
Figure 2.3 Basic configuration of a capacitive power transfer, redrawn from [22]
In [23] Graham has developed experiments to evaluate the transfer of power
and data through metal barriers simultaneously and concluded that using the
inductive coupling to power and communicate the sensor electronics is limited to
lower rate, few bps, due to the narrow the bandwidth. Experiment showed that up
to 100 bps can be transmitted when a stainless steel plate of 20 mm is in the middle
of the coils.
It can be summarized that it is possible to wirelessly transmit power and data
with electromagnetic waves. However, the power efficiency and the data rate
communication are strongly affected by the low RF penetration inside the material
[24] and the operation frequency. The propagation using acoustic waves, otherwise,
does not suffer such specific attenuation through metal barriers, as electromagnetic
wave does, becoming then attractive for use in power and data transfer.
24
2.2 Wireless power and data transmission based on acoustic waves
Communications using acoustic waves have first started in 1945 at the Naval
Underwater Sound Laboratory. This first application was developed to
communicate with submerged submarines [25] using a carrier wave of 8.3 kHz.
This solution was adopted because electromagnetic waves are extremely absorbed
in conductive medium such as sea water. The absorption rate in this condition is 45
√f dB per kilometer, where f is in Hertz. That publications also shows that the
attenuation is much lower for the acoustic waves, approximately three orders of
magnitude. Other application widely used which helped to boost the growth of
acoustic waves, mainly the ultrasonic waves, was the biomedical industry, for
instance, the ultrasound-based diagnostic imaging technique (ultrasonography) [26]
and wireless power and data communication of devices located inside the human
body [27]. Comparing with the methods to communicate through a metal layer, the
biomedical application and the underwater acoustic communication already have a
long period of research, being in a mature state of development [124-128].
The first design which used the ul trasonic waves to power and communicate with
sensors through metal was presented in a Connor et al. Patent in 1997 [90]. This is
comprised by two co-aligned PZTs attached on a solid metal wall, the outside PZT
transducer is exci ted with a continuous wave (CW) electrical signal, the t ransducer
convert the elect rical signal into ultrasonic vibrations that propagates through the
metal. The second PZT transducer located inside, receives the ul trasonic wave and
re-converts i t to an elect rical signal. The energy received in the insi de transducer
powers a sensor and it s associated electronics. The communication of the sensor
data between the inside and the outside is performed using the principle of
impedance modulat ion. A transistor is connected in parallel with the electrical
terminals of the inside transducer, acting as an electronic swi tch. Opening and
closing the transistor changes the acoust ic impedance of the PZT transducer,
reflecting more or less acoustic energy. The variation in the impedance impacts the
amplitude of the CW carrier which in turn can be interpreted as an ampli tude
modulation. By this means, the sensors can transmit the information which is
demodulated by an outside ci rcuit. Nevertheless, the author does not provide
25
characterization about the power efficiency and data rate capability neither the
hardware used to modulate and demodulate the sensor data.
Many research groups [12, 17-51] utilize the configuration of a pair of PZTs
coaxially aligned and attached directly to opposite sides of the metal layer. Fig. 2.4
shows a diagram of this configuration. Moreover, these works have different
approaches. Some of them focus on transmit power alone [28-40, 45], while others
focus on transmit data alone [41-44,46-52], and in some case they focus on
simultaneous transmit power and data [53-71].
Figure 2.4 Configuration of 2 PZT transducers co-aligned an attached to the metal wall,
redrawn from [67]
One of the first publication to analyze the use of PZTs to transmit energy
through a metal layer was Hu et al. [28]. In this, they examined the feasibility of
transmitting acoustic energy using the configuration of Fig. 2.4 without the need of
coupling layer. The authors have presented a mathematical formulation for a
thickness-stretch vibration when a harmonic electric voltage source drives the
transmitting PZT. This study revealed that the voltage efficiency of the system is
magnified at the first several resonant frequencies and the greatest magnification
does not occur at the fundamental resonant frequency. Numerical simulations
showed the behavior of the system varying the operating frequency and the input
admittance when varying a load impedance connected to the receive PZT.
Next, several papers with physical and mathematical modeling of power
transmission through metal layer using different transducers shapes and vibration
modes were followed. In [29-30], a cylindrical metallic layer with a pair of shell
26
shape piezoelectric transducers concentrically aligned on its inside and the outside
surfaces is modeled by means of elastic and piezoelectric theory addressed in
cylindrical coordinates. The paper also shown that energy transfer is sensitive to the
geometric and physical parameters of the structure. Hu et al. [31-32] showed that
the power efficiency is dependent on the operating frequency, the mechanical
properties of the PZTs and the electrical load viewed by the transducer. Therefore,
a careful circuit design has to be developed to acquire good energy harvesting on
the isolated side. These papers have addressed the problem by formulating
mathematical models and verified them only by numerical results; no experimental
tests were realized in them.
Sherrit et al. [33] proposed a network model of the acoustic-electric channel
based on the equivalent impedance of the system elements (Piezoelectric transducer
and metal layer) to study the power transfer efficiency based on Hu et al. [28]
configuration. This model has the advantage of being easily expanded to account
additional acoustic elements such as insulation layer and coupling layer.
In [34] different methods to attach the transducers on the metal were studied. The
coupl ing methods include bolted with a backing structure, clamped with grease
couplant and by at taching using a conductive epoxy. With 53% of measured power
efficiency the method using clamp and grease obtained the highest efficiency
fol lowed by the conductive epoxy that gave 40% of efficiency.
Experimental results of [35, 36] showed that high power can be delivery
through metal plates. Two experiments with distinct thickness of a metal barrier
were evaluated, the first provides 100W through 3.4mm thick titanium plate and
the second provides 1083W through a 5mm thick metal barrier. The latter is the
highest reported power transfer achieved on the literature. This was possible by
using a stack of four PZTs with a total thick of 13.6 mm in which the system present
its resonant frequency at 24.5kHz obtaining an efficiency of 84%.
Kiziroglou et al. [45] have transmitted power along a pipe with 1m of distance
between PZTs transducers, using acoustic transversal waves. The used PZT disk
transducer has a nominal radial resonance of 50 kHz and the system was able to
deliver approximately 18mW of power when 20W is applied on the transmitter. An
analysis of the power transfer in the presence of water inside the pipe shows a
decrease of the power as the fluid increases the attenuation of vibration throughout
the spectrum, when using this configuration, mainly because part of the acoustic
27
energy leaks to the water. Nevertheless, the system delivered 4mW when 20W was
applied. Previously studies have shown that the power transfer is affected by the
electrical reflection between the signal generator and the PZT transducer. In [60], a
simultaneous conjugate impedance matching was analyzed as a method to improve
the power transfer. The experimental results have shown a 55% of efficiency with
81 W of power being transmitted through the channel.
Up to here the above references have focused on wireless power delivery
through metal layers. Some research groups however developed studies mainly on
data communication through metal for enclosed sensors. The first report to do such
analysis is dated 2000 by Hobart et al [41]; they have developed a device for
transmitting data through a ship’s hull. Payton, on the other hand, creates a patent
titled “System for acoustically passing electrical signals through a hull” [42]
describing the use of two pairs of piezoelectric transducer in which one of them is
in charge of forward transmission and the other of reverse transmission. The patent
does not specify if an experimental test was realized.
At about the same time in 2006, a research group at Rensselaer Polytechnic
Institute (RPI) initiated the study of wireless ultrasonic data transmission through
metal layers. The first work is the master`s thesis of Murphy [43] which investigated
methods for sensor monitoring inside a sealed pressure vessel. Three configurations
were created; a “single-hop”, Fig. 2.5 (a), which uses an unidirectional data
transmission, a “double-hop”, Fig. 2.5 (b), which is a full-duplex system with
separated forward and reverse transmission, and a bidirectional data transmission
named “reflected-power”, Fig. 2.5 (c), which uses the variation of the transducer
impedance to communicate. Data rate of 500 bps, 5 kbps and 300 bps was
respectively achieved for the three configurations on a 148 mm thick steel layer.
Thereafter, Saulnier, et al [44] have developed a configuration that merges the
“double-hop” and “reflected-power” configurations. This was able to communicate
with a sensor at a rate of 500 bps through a 152.4 mm thick steel.
28
Figure 2.5 (a) Single-hop (b) Double-hop and (c) reflected-power configuration,
redrawn from [43]
29
Other group who was dedicated to study the through metal data transmission
was at Drexel University. The target of the group was not for enclosed sensors but
for repeating data across metal compartments of naval vessels. Some techniques
described are the communication based on the echo-cancellation to suppress the
channel reverberation [46], pulse amplitude modulation [47] and a scheme using
the orthogonal frequency-division multiplexing (OFDM) [48-51-33]. In the
investigated methods, they developed digital communication to improve data rate,
from 50 kbps to 30 Mbps. Other application that uses the acoustic waves was
developed by Hosman et al. [52] based on multi-tone frequency-shi ft keying
(MFSK) to communicate with devices located inside a shipping container. The
system was able to transmit low data at a rate of 360 bps.
Concurrently, research has focused on simultaneously wireless power and
data transmission through metals layer. The Australian Defense Science
Technology Organization developed and evaluated methods to deliver power and
data transmission through metal plate for health monitoring sensors embedded
within aircrafts. They presented an equivalent model based on Pspice that uses the
analogy between the second order acoustic waves differential equations and the
second order electrical transmission line equations [37,38]. The Pspice model
implemented by Moss et al. in [37,38] was based on the thickness-mode transducer
firstly presented by Leach [72] and subsequently extended by Püttmer et al. [73] to
introduce a lossy transmission line considering transducers mechanical losses.
Moss et al. also performed experiments which shown that 300mW of power can be
wireless transmitted through an aluminum plate with thickness in the range of
1.6mm to 5mm at an efficiency of 30% using a nominal transducer of 1MHz in
thickness-mode vibration. Further publications also include power and data
transmission simultaneously. In [39,40] the described system is able to transmit
420mW of power through an aluminum plate of 1.6mm thick, representing a
efficiency of 42%, as well as a data rate of 115 kbps.
Aeronautic and aerospace applications helped to foster groups such as EADS
Innovation Works, University of Paderborn, and Saarland University [53,54,55].
They have studied remote ultrasonic power and data transmission for sensors inside
metal containers. One of the application uses a pair of thickness-mode transducer
30
“sandwiched” attached to a 7 mm thick aluminum barrier, following the
configuration of figure 2.6.
Figure 2.6 Power and data communication of a sensor inside metall ic envelope, redrawn
from [53]
The energy that is received in the wireless sensor (WS), which is isolated
from the data concentrator (DC) by a metallic envelope supplies power to a digital
processor and a digital sensor. The system has a half-duplex bidirectional
communication, where in the WS-DC way the digital processor modulates the load
coupled to the RX transducer. On the other hand, the DC-WC communication
modulates the amplitude of the carrier signal. It has been demonstrated that the
system can delivery 30mW of power through the 7 mm thick aluminum layer and
a data communication of 1 kbps was achieved.
The research group at RPI, previously mentioned, has also extensively
worked on the methods to simultaneously wireless transmit power and data through
metal using acoustic waves. They addressed some important issues such as full-
system prototypes evaluations [56,67], models of the acoustic-electric channel
[57,59,63,69], high-data-rate communication [62,63,65], apparatus and methods to
maximize the efficiency of power and data transfer [60,63,64] and different types
of configurations and methods [61,68,69] Shoudy et al. [56] developed a prototype
based on the diagram of Fig. 2.4 in which the communication uses the “reflected-
power” with a pair of transducers operating at 1 MHz. The CW signal generated in
the “outside” is transmitted to the “inside”, where it is rectified and regulated to
supply the sensors and peripheral circuitry. Additionaly, an electric switch varies
the impedance of the inside transducer and consequently changes the amplitude of
the CW signal. Experimental results have shown that the inside circuitry can harvest
250 mW of power, and reliable communication at rates of up to 55 kbps with 57
31
mm thick steel was achieved. In [67] the development of a prototype shows the
acoustic power and data communication through a curved metal layer with 3.2mm
of thickness. The developed experiment has a low-power microcontroller located
in the “inside” and operating passively. The author has also developed the boards
of “inside” and “outside”. The system shows the feasibility of transmitting data at
10 kbps using amplitude modulation, with 0.02% of packet loss. Nevertheless,
information on power consumption of the inside electronics was not provided and
the sole component to be powered was a microcontroller.
The RPI group has been studying models to simulate the system based on Fig.
2.4. A finite element model of the system was used to characterize the impedance
of the PZT transducer when attached on the metal layer, showing high correlation
between the model and the experimental characterization [67]. In [68] many
parameters concerning the power transfer of the ultrasonic channel were simulated,
for instance, the transducer area, the metal wall thickness and compositions and the
transducer-wall coupling effects and, strong agreement with experiments were
obtained. Furthermore, Lawry et al [69] developed an analytical model based on
ABCD parameters for the sandwiched plate configuration of Fig. 2.4. The ABCD
matrix represent the layers of the acoustic-electric channel, comprising the
transducer and the intermediate layer, such as metals, couplants and fluids. The
enhanced model shows great performance while reducing the complexity of finite
element method. More recently, Wilt et al. [75] have developed a model that
represent the layers of the acoustic-electric channel by a two-by-two travelling
pressure wave transfer matrix related with the forward and reverse pressure waves
on both faces of each layers. A comparison of the model with an experiment
consisting of two co-aligned transducer and attached on stainless steel block, 74.8
mm thick, shows that the model is capable to reproduce the behavior of physical
channels. It is also shown that the piezoelectric transducer model is compatible with
the ABCD model, allowing the connection with electronic components.
The RPI group also explored different configurations to evaluate the behavior
of acoustic power and data transfer. Lawry et al. proposed [56-69] A novel
configuration formed by two pairs of piezoelectric transducers, one of them
operating at 1MHz with 66.7 mm of diameter and the other operating at 4 MHz with
25.4 mm of diameter transmit power and data separately. The transducer with lower
32
frequency transmits the power and the other, the data. A communication protocol
based on OFDM turns the system into a high data-rate transmitter with a high
spectral efficiency. The experiment reveals a communication data rate of 17.37
Mbps with 50 W of delivery power through a 63.5mm thick steel. In [61], Lawry et
al have built an experimental setup for high-temperature applications. The high
temperature piezoelectric transducers were attached with a high temperature
couplant and a clamp in order to operate inside a chamber with temperatures up to
260°C. The method of data communication is based on “reflected-power”. The
results shown that the system is capable to transmit data at a rate of 50 kbps from
the inside to outside with 1W of power transmission. A different configuration
formed by a pair of coaxially aligned PZTs and a third PZT attached on the outside
is simulated using an equivalent circuit based on Pspice® simulation [69]. In this
publication an analysis of the power and data communication were performed with
good agreement with experiment results. The RPI group also explored a multilayer
channel that consists of a steel-water-steel [68] with 15.97 mm, 88.3 mm and 10.92
mm thick, respectively. The system was analyzed by S-parameters and tested
experimentally showing that a data rate of 4 Mbps and a power transfer efficiency
of 30 % is possible. This work is the only one that evaluates the power and data
communication passing through metal and water multi-layers, showing an appeal
to improve the studies that explores a multilayered configuration. Furthermore, the
publication did not explore the feasibility of the system when exposed to high power
or long periods of operating.
With a different approach, a group at Newcastle University utilized
electromagnetic acoustic transducers (EMATs) to generate the acoustic waves
inside the metal [5, 52, and 53]. They achieved 1 Mbps of data rate through 25.4
mm thick metal with a transducer liftoff of 0.8 mm to the metal surface. However,
the use of EMATs are very inefficient to transfer power due to its low electro-
mechanical coupling. On the other hand, it has an extremely advantage of not
requiring direct contact with the metal suppressing the use of couplants.
Comparing the methods to power and transmit data through a metal barrier it
is possible to conclude that electromagnetic coupling are suitable for applications
where the metal layer is thin and the data rate low. Ultrasonic waves otherwise have
the ability to propagate inside metal with more efficiency and with high power and
data transmission rates capabilities. However, historical review showed limited
33
experiments that explore the development of prototypes with sensors and
peripherals circuitry. Some challenges need to be solved for a proper engineering
application. Studies about the long-term reliability and efficiency of the epoxies and
coupling layers is one of the known drawbacks of the ultrasonic system based on
PZTs transducers. Other possible problem is the influence of the temperature,
pressure and other parameters in the system, rarely investigated. This survey also
clarified that the choice of setup depends on the application as there is no optimum
solution regarding both power and data communication. A specific application can
be focused on achieving high data communication rates, or high power supply, or
even concern a high temperature scenario. All of these issues require specific
solution and all of them are in constant evolution.
3 Analytical and numerical design
This section describes the overall system adopted in this work and two models
used to simulate it; one based on Pspice electric circuit simulation and one
analytical model, which has been implemented in MATLAB®. Three major blocks
are present in the system; the outside block, the inside block and the acoustic
channel block, see Fig. 3.1. The outside block is composed by a signal generator,
responsible to send a carrier signal, a PZT transducer, named outside transducer,
and a circuit to demodulate the received signal. The inside block is composed by a
circuit to rectify and store the received energy, a PZT transducer, named inside
transducer, and a circuit to modulate the signal. The acoustic channel block is the
material medium connecting both sides by means of ultrasonic wave propagating
inside of it. The simplest conceivable channel consists of a metal barrier plate that
separates both PZT transducer and the acoustic couplant that attach each PZT
transducer on the metal plate, as shown in Fig. 3.1. Alternatively, the channel may
be composed by several layer, instead of just a single metal block. For instance,
there can be a metal layer and a liquid layer separating the transducers. These three
blocks form the global system that is called power and data communication through
acoustic channel, (PDAC).
Figure 3.1 Overall diagram of PDAC generic system
35
In the next sections the acoustic models implemented in PSPICE and
MATLAB are explained. This two models are studied in order to understand the
frequency and time domain behavior and characteristics of PDAC.
3.1 Pspice modeling
In order to simulate acoustic elements of the channel the approach proposed
by Roa-Prada et al. [69] is adopted here. In this approach one considers analogies
between the electric voltage and current and the sound pressure and velocity. In
order to model the system, two different categories with different formulation are
further described, the piezoelectric transducer and the intermediate layer.
3.1.1 3.1.1 Piezoelectric transducer model
The piezoelectric transducer can be modeled as a three port device with one
electrical port and two mechanical ports. The electric signal is applied or sensed in
the electrical port, whereas the two mechanical ports represent the front and back
faces of transducer, which vibrate when mechanical waves are generated or sensed.
As the analytical solution for this system is complex mainly due to the
electromechanical analysis, an analogous model expressed in the electrical domain
can be more practical and convenient. In this context, Leach [72] has built a model
using transmission lines and controlled-source for piezoelectric transducer, Püttmer
et al. [73] insert a lossy transmission line considering mechanical losses in the
piezoelectric transducer and Deventer et al. [74] implemented a low loss
approximation to model piezoelectric transducer. In this work the part of the model
which specifically model the piezoelectric transducer is based on the thickness-
mode transducer that Leach [72] has developed.
The diagram of the piezoelectric transducer illustrated in Fig. 3.2 shows two
mechanical ports represented by force-velocity pair and one electrical port
36
represented by voltage-current pair. Eq. (1)-(3) are the governing equations of this
model. These are based on mechanical-electric relationship of a piezoelectric
material.
Figure 3.2 Diagram of the piezoelectric transducer
(1)
(2)
(3)
ρ is the densi ty, A the transducer cross-sectional area, c is the relative elast ic
constant, whose common uni t is (N/m²), h is the piezoelectric constant whose
common unit is (Nm4/C), ε is the permittivi ty whose common unit is (F/m), E is the
electric field intensity, D is the flux density, ζ is the particle displacement , u is the
particle velocity, f is the force, i is the current from the electrical signal and z i s the
coordinate where the thickness of the t ransducer is distributed.
Equations (1)-(3) are described in the frequency domain, in which an implicit
Laplace Transform is considered. According to the Laplace Transform derivative
and integration properties [76], a multiplication by “s” in the frequency domain
37
represents a time differentiation in the time domain, whereas a division by “s” in
the frequency domain means time integration in the time domain.
Being i the current which flows in the external electrodes of transducer, q the
charge related by the equation q = I/s and the flux density D = I/(sA), the equations
(1) and (2) can be rewritten as:
(4)
(5)
Drawing a parallel with telegraphist's equations [77] and manipulating the
equations (1) and (2) one can obtain a relationship between transmission line and
piezoelectric parameters. The telegraphist's equations are
(6)
(7)
where the voltage V is analogous to [f – (h/s)i] and the current I is analogous to the
particle velocity u. L and C are the distributed inductance and capacitance,
respectively. The relationships between parameters of transmission line and the
piezoelectric transducer equations are
(8.a) (8.b)
The phase velocity of the lossless transmission line is:
(9)
Substituting the values of L and C in Eq. (9), the phase speed of the piezoelectric
transducer is
38
(10)
Using the same principle for the characteristic impedance of a transmission line,
(11)
The characteristic impedance of the piezoelectric transducer can be obtained
substituting the analogous values of L and C, from Eq. (8), and the expression of
phase speed from Eq. (10), leading to
(12)
Making the capacitor per unit of length of Eq. (8.b) in funct ion of the phase speed,
from Eq. (10), instead of the relat ive elastic constant, imply that
C = 1/(Azρu²p) (13)
The last analogy equation can be obtained integrating Eq. (3) from z = 0 to z = lz
and letting D = i/(sA) and ζ = u/s. T he result is the vol tage across the transducer
electrodes, which assumes the expression
(14)
where u1 = u(0), u2 = u(lz), and C0 is defined as
C0 = εA/lz. (15)
In order to build a circuit that can be designed in PSPICE, the transducer has
to be modeled in two parts. The first one as a transmission line using the electrical
and mechanical analogies and the relationship with the telegraphist's equation, and
the second one by the electrical-mechanical coupling which is described by the Eq.
(14).
As illustrated in Fig. 3.3(a)., T represents the transmission line, F1 and F2 the
forces on the faces of transducer and u1 and u2 the particle velocities. In Fig. 3.3(b),
there is a voltage V that is applied on the transducer and a capacitor C0, related to
the area, thickness and dielectric of PZT transducer, according to Eq. (14).
There are two current-control led vol tage sources in Fig. 3.3. These sources
represent the coupling between the mechanical and the electrical part. The
39
mechanical part (Fig. 3.3.a) has a voltage source controlled by the injected current
i. On the other hand, the elect rical part (Fig. 3.3.b), presents the velocity difference
(u1 – u2) as the “current”-controller.
Figure 3.3 (a) Transmission line representing the mechanical part controlled by the
current (i) and (b) the electrical part of the transducer controlled by the particle velocity
Having the design of the circuit, it is possible to implement it using an
electrical simulation software. In this dissertation ORCAD 9.2 [88] was chosen
since it has many PSPICE model and it is simple to manage. Fig 3.4 shows the
analogous subcircuit for the thickness mode transducer created in ORCAD software
which was obtained from the piezoelectric transducer from Fig. 3.3.
Figure 3.4 Transducer subcircuit schematic in ORCAD software
The electrical port (EP) in Fig. 3.4, represents the input/output voltage
applied/sensed on the transducer. Connecting it with capacitor C0 and current
controlled source F1, it has exactly the same function of the electrical part,
illustrated in Fig. 3.3 (b). The reason to choose this current controlled source instead
of voltage controlled source, is to avoid the use of complex variable s, since PSPICE
40
does not have an element capable to treat it. This operation can be straightforward
obtained by using the Norton-Thévenin equivalency [78]. The mechanical part,
illustrated in Fig 3.3 (a) is added in the circuit of Fig. 3.4 by the parts: F2, RS, CS
and E1. In this context, it is possible to substitute the 1/s term in the transfer function
of E1 by an integration operation, according to the Laplace Transform properties
[76], which can be done by a capacitor, producing a electrical voltage
(16)
For Cs = 1 F, the dependent voltage source E1 is equal to h multiplied by the
integral of the current injected in port EP. The resistor RS is included to prevent the
terminal of CS to float, imposing a current path. For RS equals to 1 kΩ, the RC time
constant is several times greater than the transducer resonant frequency, not
affecting then the time and frequency response. The front face of the transmission
line, representing the second mechanical port (MP), is left opened to be connected
to the next layer, which is the intermediate layer subcircuit. As the transmission line
(T) from Fig. 3.4 represents the transducer, the length of the transmission line is
equal to transducer thickness.
The back face of the transmission line is shorted with a resistor, Rb, that
represents the mechanical impedance of the transducer back layer, in this case it is
assumed to be air. Other resistor that appears in the circuit, Rd, is related to a
complex dielectric loss. This other losses implemented in the model will be
discussed in section 3.3. As one can see, a few number of elements are used to
model the transducer. As acoustic impedance is associated with acoustic pressure,
and the mechanical-electrical analogy relates force and voltage, and not pressure.
The characteristic impedance of the mechanical layer has to be properly
transformed in order to satisfy the relationship [3]. Equation (17) shows the
relationship between force (F) and pressure (P).
(17)
Analogously, the characteristic impedance can be rewritten multiplying the
equation by the cross-section area as:
(18)
41
Table 3.1 shows characteristics impedances from common materials used as
mechanical layers [6].
Table 3.1 characteristic impedances of common materials
Material Z(MRayl)
Air 403x10-3
Aluminum 17.33
Steel 45.7
Water 1.494
Completion fluid1 ~2.8
3.1.2 3.1.2 Intermediate layer model
The intermediate layer can also be modeled by acoustic-electric analogies.
Deventer [74] applied the approach of Püttmer [73] for liquids and solids to obtain
an equivalent electrical circuit of acoustic waves propagation through materials. In
this context, a comparison was made between electrical and mechanical domain
also using the telegraphist's differential Eq.(19) and the acoustic wave different ial
Eq. (20), respectively:
(19)
1Fluid use in wellbore after the drilling [100]
42
(20)
where γ is the propagation constant associated with the change of amplitude and
phase of electromagnetic waves as it propagates in a material, and kc is acoustic the
complex wave number, represented in Eq. (21) and (22), respectively.
(21)
(22)
where R´, L´, G´ and C´ are the elements of the transmission line per unit length, w
is the angular frequency and τ is the relaxation time [3]. Using the low-loss
condition where wL’ >> R’, wC’ >> G’ and 1 >> wτ, the Eq. (23) and (24) can be
rewritten as:
(23)
(24)
With real part, αe, being an attenuation constant of the propagation constant
and αm the attenuation of the complex wave number. The imaginary part, β and κ,
the phase constant and wave number, respectively.
Finally, the imaginaries parts are obtained applying the low loss approximation,
(25)
Equaling β and κ gives the phase velocity of the intermediate layer in function
of transmission line parameters L’ and C’.
(26)
Using another analogy relationship, this one between the electrical and
mechanical characteristic impedance we can assign:
(27)
43
And for the lossy acoustic medium , Zac [6]:
(28)
where the subscripts el and ac stand for electric and acoustic, respectively.
Considering a low-loss approximation, the electrical and mechanical characteristics
impedances become:
(29)
(30)
Using the same principle from transducer model in which the force, and not
pressure, is represented by voltage. The equivalence between the two characteristic
impedance is simply
(31)
Using the equations (26), (27), (28) and the relationship equation (31), one
can assign the following relationships:
(32)
(33)
With Eq. (8) to (33), one can model in PSPICE an equivalent circuit of the
piezoelectric transducer, as well as, an intermediate layer. The transducer may be
of any piezoelectric material, whereas the intermediate layer can assume any
acoustic material, either a metal or fluid, or even a cascade combination of many
different layers. The circuit analogies between electric and acoustic elements are
summarized in Table 3.2 for the piezoelectric transducer and in Table 3.3 for the
intermediate layer.
Table 3.2 Analogies between mechanical and electrical of PZT transducer
Electrical Mechanical
V [f – (h/s)i]
I u
L' ρAz
C' 1/(Azρup²)
44
Table 3.3 Analogies between mechanical and electrical of intermediate layers
Electrical Mechanical
V f
I u
L' ρAz
C' 1/(Azρup²)
The model of piezoelectric transducer is straightforward obtained if all
parameters are known, however this task could be sometimes challenging. The
intermediate layer, on the other hand, models all the layer that are not piezoelectric
as a transmission line. Acoustic propagation in solids and fluids can be modeled
using this approach, considering that the relevant wave propagation occurs in one
direction by a single acoustic wave mode.
3.1.3 3.1.3 Pspice loss considerations
Up to here, the model presents the electrical parameters that have the
equivalence to the acoustic equations, however for a more realistic model a loss
considerations is introduced in this section. As demonstrated by Deventer [74] and
Püttmer [73], a lossy transmission line is used to model transducers and
intermediate layers introducing a resistive element in both transmission lines, which
represents the loss factor of the transducer and intermediate layer. This resistance
can be calculated using the real part of the complex propagation constant γ, which
is the attenuation coefficient α of the transmission line. With a low loss
approximation one assumes that G' = 0 and wL' >> R' and the complex propagation
constant given in Eq. (23), can be divided in two different approach, one concerning
the piezoelectric transducer and other the intermediate layer.
a) Piezoelectric transducer
Considering a low loss approximation, the complex propagation constant of
the transmission line can be approximated by the low order terms of Taylor series
45
expansion of (25). The real part, which is the attenuation coefficient, is then
simplified to
(34)
Knowing that in a series RLC circuit, the quality factor,( Q, which represents
the ratio of the energy stored to the energy dissipated, is described as:
(35)
where δφ is the mechanical loss factor of the piezoelectric transducer. Most
manufactures provide the mechanical loss factor δφ in their material datasheet as the
inverse of the mechanical quality factor Q.
Therefore, the attenuation coefficient can be rewritten as
(36)
Note that one can write the R’ parameter as:
(37)
Other loss that impacts the performance of the transducer is the dielectric loss.
This loss can be explained since the capacitance C0 has a complex dielectric loss,
which can be modeled using a resistor, Rd, in parallel with C0, with value:
(38)
It is worth highlighting that PSPICE simulators allow only constant values
for R, therefore an approximate value can be obtained using ω fixed and equals to
the resonance frequency of the piezoelectric transducer.
b) Intermediate layer
The intermediate layer loss, is a combination of viscous losses and diffraction
losses. Using the same approach from piezoelectric transducer loss, the viscous loss
part of R' can be determined making the same low loss approximation, however
using the relationship with attenuation coefficient instead of loss factor. . The R'
46
from the transmission line is obtained from Eq. (34), substituting L' and C’ by its
mechanical equivalence:
(39)
the coefficient αv account for the attenuation due to viscous losses in (Np/m).
The diffraction part of R' represents a phenomenon that occurs inside a thick
material layer, when the piezoelectric transducer area is smaller than the surface
area of intermediate layer [79]. This loss can be understood as an amount of
ultrasonic energy that spreads from the center axis that separates both transducers
as illustrated in Fig. 3.5..
Figure 3.5 Spreading attenuation of acoustic wave
Bass [80] formulated an expression for the ratio of the average energy on the
receiver transducer to the average energy at the transmitter transducer. The
spreading attenuation is expressed as:
(40)
Where pr and pt stand for the intensity pressure received on the receiver
transducer and the intensity pressure transmitted by the transmitter transducer. The
ratio of their squares is approximately equal to
(41)
the dummy variable ξ is defined as:
(42)
47
The attenuation αs can be expressed in dB/m or Np/m, by knowing that one
Neper is equal to 8.6858 dB. The effective attenuation is a sum of the viscous loss
and the spreading loss. The quantity of spreading attenuation can be incorporated
in the R' element of transmission line, being the total loss coefficient equal to:
(43)
With this three types of losses we can implement the model of the transducer
and intermediate layer in PSPICE with proper accuracy. The introduced losses are
however low loss approximation models. In the next sections an explanation of the
overall system used is described and some simulations of this system are performed.
3.1.4 3.1.3 Full system model
Gathering the piezoelectric transducer and the intermediate model, it is
possible to build an equivalent circuit that covers all the mechanical and electrical
parts. In Fig. 3.6 a full system is designed using ORCAD software, with transducer
blocks representing the transducer model and the metal and adhesive transmission
lines representing the intermediate layer.
Figure 3.6 Full system circuit designed in ORCAD
Parameters used to build the transducer and intermediate layer are shown in
Table 3.4. These values of piezoelectric transducer are obtained from PI Ceramic
material [81] data sheet and complemented with piezoelectric ceramic equations of
characterization [84]. The intermediate layers properties from adhesive
48
(Huntsman® Araldite 2015) and aluminum are obtained using materials
datasheet[82]and literature reference[83].
Table 3.4 Materials properties
Transducer Properties Value
At(mm²) 400
ε33(t)/ε0 1200
k33 0.66
kt 0.46
ρt(Kg/m³) 7800
Q 2000
c33(d)(N/m²) 16.6E10
tand 3x10-3
Adhesive Properties Value
At(mm²) 400
ρa(Kg/m³) 1400
va(m/s) 2100
α(dB/m) 1500
Metal Properties Value
At(mm²) 400
ρm(Kg/m³) 2700
vm(m/s) 6420
α(dB/m) 2
49
3.1.5 3.1.4 Analysis of power transfer
Analyze how the energy pass through the metal is one of the essential scopes
of this dissertation. As one can see in Fig. 3.7, the implemented system is
represented by two transducer blocks and three transmission lines. A frequency
domain analysis using S-parameters [85] is then performed to study the
characteristics of power transfer between transducers.
Figure 3.7 Acoustic channel with S11 and S21 blocks represented in blue and red,
respectively
Scattering parameters, which are commonly referred to as S-parameters, is
related to the traveling waves that are emitted or reflected in a network with n-ports.
In other words, this means that with S-parameters we can measure the quantity of
power that is incident/reflected in one port and reflected/incident from the same
port or from another port. Figure 3.8 illustrates this system containing two ports.
Figure 3.8 Two-port configuration of S-parameters
Therefore, we can define the individual S-parameter coefficients S11.S12,
S21 and S22 as a function of the incident and reflected waves, according to Table
3.5.2.
50
Table 3.5 2-port S-parameters
S11 V1- / V1
+
S12 V1-/ V2
+
S21 V2-/ V1
+
S22 V2- / V2
+
To transform these voltage coefficients into power coefficients, there is a
commonly used expression that relates the gain in V/V to dB:
(44)
To perform the analysis in ORCAD, a linear AC sweep analysis with
frequency range from 1 to 4 MHz containing 1601 points is generated [86]. With
S21 and S11, one can extract some characteristics of power transfer and reflections
of acoustic waves, respectively. In order to obtain these values in SPICE one can
connect to the input and output terminals of a two-port components specific circuits
specially designed for this purpose, as proposed in [99]. These circuits are shown
in Fig. 3.7, the left one highlighted in blue obtains the S11 and the right highlighted
in red the S21.
3.1.6 3.1.5 Analysis of Data Communication
Other fundamental study, is a time domain analysis. This type of analysis is
used in order to investigate how data communication develops. As we switch the
terminal load of the output PZT transducer between two values, a change in the
input impedance seen by the generator is obtained, leading to an increase or
decrease of the reflected waves. In the generator side this can be interpreted as a
variation of the signal's amplitude or, as an amplitude modulation (AM).
The PZT transducer has a mechanical characteristic impedance that depends
of stiffness (C33) and the phase velocity (up), expressed in Eq. (30). The stiffness,
otherwise known as elastic constant, can assume two distinct values represented by
51
the parameter (CD
33) and (CE
33). The difference between them is exactly what can
be used to perform amplitude modulation, as the parameter (CD
33) refers to a
constant elastic when the electrodes are open-circuited and the parameter (CE
33)
refers to a constant elastic when the electrodes are short-circuited [87]. Accordingly
to this, two resistance element can be connected in parallel to the electrodes of the
PZT transducer to act as an open-circuited or a short-circuited.
A transient analysis in Pspice shows a curve in time of the amplitude
modulation on the outside transducer. To realize this simulation in Pspice, a circuit
called modulation block is built. The modulation block represented in Fig. 3.9
switches the terminal load of the output transducer into two distinct values, in this
case between R1=50 Ω and R2=0.22 Ω. These values are chosen to simulate a load
when the inside PZT are providing power to the inside block and when the inside
PZT is short-circuited with a MOSFET transistor with 0.22 Ω of Rds(on).
3.2 Analytical modeling
An analytical analysis of the same system described in the previous section
can be implemented with technical computer software. Lawry [63] has designed
an analytical model of a co-axially aligned piezoelectric transducer using the
transfer matrix method with mixed-domain two-port ABCD matrices.
The same parameters for the both transducers, adhesive layer, metal layer and
transducer backing layer used in Pspice are used in the analytical model, which was
implemented using MATLAB®. This model is more realistic because it has both
frequency dependent parameters and complex coefficient, which cannot be used in
PSPICE.
Figure 3.9 Modulation block
52
3.2.1 Two-port ABCD Matrix
One form of representing the piezoelectric transducer and the intermediate
layer is to use cascaded two-port ABCD matrices. The acoustic channel can be
modeled by a series multiplication of the different types of ABCD matrix, in which
each matrix represent a layer of the channel. Lawry [63] proposed this type of
transfer matrix to model the electro-mechanical, purely mechanical and purely
electrical layers using the analogy between electrical voltage(V) and mechanical
force (F) and between mechanical particle velocity(u) and electrical current (I).
Therefore, there are four kinds of ABCD matrix of interest for modeling the whole
acoustic channel, given by
45)
(46)
(47)
(48)
The subscripts (m) and (e) specify which type of ABCD matrix it is
representing, in which m stands for mechanical and e for electrical. Thus the
possible matrices represent a layer in which its ports are of following kinds:
mechanical-mechanical ports, electrical-mechanical ports, mechanical-electrical
ports or electrical-electrical ports. Therefore, it is possible to represent all sub
systems of the channel by a two port ABCD matrix.
53
3.2.2 Piezoelectric transducer model
Royer [92] introduced the concept of impedance matrix, considering a one-
dimensional model of a bulk piezoelectric. The analytical model uses the same
approach based on the wave equation as the one adopted in PSPICE for treating the
transducer. Therefore, it has the same number of ports to represent the transducer
as the previous presented model, i.e., two mechanical and one electrical. Fig. 3.10
illustrates the cross section of piezoelectric plate transducers. In which an electric
voltage is injected in electric port generating mechanical waves that propagate
inside the transducer. The model only predicts one-dimensional propagation, in this
case, in z direction. On each boundary of the transducer there is a mechanical port
represented by the particle velocity and the force. Connecting the transducers
mechanical port to an adjacent mechanical port can produce forward and backward
waves, illustrated in Fig. 10, if the materials have distinct characteristic impedances.
Figure 3.10 Piezoelectric mechanical and electrical ports, redrawn from [63]
The mechanical ports are governed by the following equation:
(49)
where Z corresponds to the characteristic impedance multipl ied by the cross section
area.
Expressing this equat ion in terms of velocities at both faces, implies:
54
(50)
(51)
This two forces are the forces at the two mechanical ports of the piezoelectric
transducer. The other port is the electrical port. In this port the voltage applied
between the faces of transducer can be calculated as the integral of the electric field
E (Eq. 3) and is expressed below:
(52)
Where (z2 – z1) is the thickness of the transducer.
The impedance matrix for the piezoelectric port assumes the expression:
(53)
To accomplish the analytical analysis using ABCD matrix, it is necessary to
transform the impedance matrix of three ports into one of two ports in order to be
used as an electrical-to-mechanical 2x2 ABCD matrix. Since one of the mechanical
ports has a termination load, Zb, them the load constrains a relationship between the
voltage and current of that port. Consequently, one degree of freedom is lost. The
2x2 matrix of Eq. (54) is obtained from algebraic manipulation of Eq. (53)
(54)
Where:
55
(55)
(56)
(57)
(58)
where ϒ and C0 where previously defined in Eq. (21) and (15), respectively, and w,
h33 and d where previously defined in section 3.1.1
The constant Z, that is the modified characteristic acoustic impedance, which is
given by
(59)
Where up, ρ, and A were previously defined in section 3.1.1. One can notice
that in Eq. (59) the constant (A) refers to a cross section area that is not related to
the area (A) of Eq. (55). Another constant that appears in the matrix parameters is
Zb, illustrated in Fig.3.10, which represent the acoustic impedance in the back face
of the piezoelectric model.
One can extend this approach by considering that the acoustic channel has
two piezoelectric, one transmitting and other receiving. The model described above
shows the details of the transmitter model. For the receiving piezoelectric model,
Lawry [63] demonstrated that the model is defined by the ABCD mechanical -
electrical matrix below:
(60)
56
The elements of the receiver matrix has the following relationship with the ones of
the transmitting piezoelectric matrix:
(61)
3.2.3 Intermediate layer model
As the intermediate layer has no electrical port the ABCD matrix of this layer
has the mechanical-mechanical configuration. To model the intermediate layer,
Lawry [63] used the one-dimensional wave equation for particle displacement δ
along the z direction:
(62)
A solution for this equation is a spatial and temporal harmonic oscillation for the
particle displacement:
(63)
By deriving equation (63) one can apply the result equation at z1 and z2 , as
illustrated in Fig. 3.10, that yield the following expressions for the particle
velocities2. Both equations suppress the time oscillation term :
(64)
(65)
Manipulating the Eq. (64) and (65), considering that d is equal to z2 –z1, and solving
for a and b, yields:
2 Figure 3.10 represent the velocities with (v) variable, however to keep the notation of this
thesis, the velocities are represented by (u) variable.
57
(66)
67)
The relationship between force acting in both ports of the layer and the particle
velocity starts from the Hooke’s law [93]
(68)
where σ is the stress tensor and ε the strain tensor, and E is the stiffness tensor.
Considering a unidirectional displacement along z direction the strain tensor is only
nonzero at the normal z direction, this component is thus equal to:
(69)
The same principle applies for considering the stress sensor presenting only
one component, which is the proportional to the force according to Eq (17).
Applying (69) and (17) into (68) leads to
(70)
Expanding Eq. (70) one can express the force at any position z along the layer,
which assumes the form (suppressing time-variation) of
(71)
Eq. (71) can be wri tten in funct ion of the specific acoustic impedance (Z) as
(72)
Applying equations (66) and (67) in (72) and further rearranging the obtained
expressions to satisfy the ABCD configuration, one finally obtains the mechanical-
mechanical ABCD matrix as:
(73)
Where the subscript “1” and “2” refer to port “1” and “2” of the layer respectively.
58
3.2.4 Analytical loss considerations
Distinctly from the PSPICE model the analytical model does not use
analogies to represent the mechanical part with electrical entities. The piezoelectric
losses and the intermediate losses can be more properly formulated in the model.
As was done previously, the loss consideration is divided in two parts, piezoelectric
and intermediate layer.
a) Piezoelectric transducer
To model the losses involved in the piezoelectric transducers, it is not
common to represent the losses as a single term α, real part of the propagation
constant ϒ. Instead, it is adopted the more accurate approach with considers three
types of losses. Each of which is associated with three different piezoelectric
constants, β33, c33, h33 [94]. This approach treat loss by introducing lossy terms into
these parameters but further setting to zero the original loss term (α = 0). These
lossy parameters are:
(74)
(75)
(76)
where the tilde over the constant stand for a lossy constant, tan δ is the dielectric
loss tangent of the piezoelectric material, tan φ is the elastic loss and tan θ the
piezoelectric loss. It is also possible to represent the losses with different constants
set, namely ε33, s33 and d33.
(77)
59
(78)
(79)
where ε33T is the material’s permittivity under a constant stress, s33
E is the material’s
elastic compliance under a constant electric field, and d33 is the material’s
piezoelectric charge constant. The two set of lossy tangents are related by the
following relationship
(80)
Where kt represents the electromechanical coupling factor, thickness mode,
of the piezoelectric transducer without loss, which is defined as
(81)
Usually, the tan δ´ and tan θ´ losses did not appear in material properties.
However, the dielectric loss tangent (tan δ) is common in material datasheets of
piezoelectric transducers. The elastic loss tangent (tan φ’) is the inverse of the
mechanical usual quality factor (Q).
(82)
In this work the following set of parameters (β33), (c33) and (h33) were
adopted. Therefore, it is convenient to express tan φ in function of tan φ’, resulting
in
(83)
The implementation of this losses impacts directly on the A, B, C and D
entries of the ABCD matrix, associated in Eq. (10), (15), (21) and (59). To
demonstrate it firstly we replace equation (75) in the expression of the speed of
60
sound of the piezoelectric transducer and apply the first order Taylor series
expansion
(84)
Considering the change in the speed of sound, then β which is defined in (21)
receives a complex term and is written as
(85)
The propagation constant was modeled with the attenuation coefficient equals
to zero. However, implying the separated losses in the model transforms ϒ as
follows
(86)
The effect of the losses in the constant Z, defined in Eq. (59), is obtained by
using the new expression of Up. Thus, the constant Z can be rewritten as
(87)
Finally, to determine the impact of the losses in the constant C0 , defined in
Eq. (10), one has to express the permittivity ε33 in function of β33 as
(88)
Including these losses in the model affect on four constants presented in the
ABCD parameters, namely h33 , ϒ, Z and C0 which are then transformed into new
constants that assume complex values. The piezoelectric loss, tan θ, is normally not
provided in the material datasheet. This means that when implementing this specific
loss some kind of empirical seek for the better value should be done in order to
obtain the proper accuracy of the model, as suggested Lawry[63].
b) Intermediate layer losses
Loss in the intermediate layer is considered by extending the attenuation term
of ϒ. Since it is defined as the sum of viscoelastic attenuation constant α with the
61
solution wave number, multiplied by the imaginary unity, jβ, the diffraction loss αs
is incorporated in ϒ by adding to the formers, becoming
(89)
The diffraction loss attenuation is given by
(90)
where ls is the diffraction loss factor. Following Lawry [63] ls, can be
obtained by:
(91)
where J0 and J1 are Bessel functions of the first kind and ξ is the dummy variable
defined as:
(92)
r is the radius of the transducer.
Similar approach has been used in Pspice model to calculate the diffraction
loss, however, there a much simpler equation has been adopted related to the ratio
of energy received with energy transmitted on the transducers recall Eq. 41.
The diffraction loss of the analytical model is frequency dependent, which is not
possible to be implemented in Pspice due to a limitation in the model.
3.2.5 Analysis of power transfer
As explained in section 3.1.5, for the Pspice mode, evaluations of S-
parameters is required to analyze the power transfer of the PDAC system. The main
element of the analytical model is the global system ABCD matrix. This is obtained
by the multiplication of the individual sub-system ABCD matrices of each layer.
The global matrix, which is indeed an electrical-electrical matrix as it begins and
ends with the electrical port of both, emitter and receiver, transducers, can be used
in order to obtain the S-parameters matrix. Freckey [95] showed that the parameters
of ABCD matrix can be converted to S-parameters as follows,
62
(93)
(94)
(95)
(96)
Where Zi and Zo represent the complex electrical impedances of inside and
outside ports, respectively and Ri and Ro represent the real part of Zi and Zo ,
respectively.
The S parameters have the advantage to be defined in terms of incident and
reflected power, as commented in section 3.1.5. Using (93)-(96) it is then possible
to evaluate the power transfer of the whole channel modeled with the analytical
model.
3.2.6 Analysis of data communication
The data communication analysis has the same purpose of section 3.1.6. For
the ABCD matrix approach, the input voltage can be obtained by connecting the
global ABCD matrix in series with a 50 Ω, which represents the output load from
the voltage source, as illustrated in Fig. 3.11. The electrical-electrical 2-port ABCD
configuration allows the cascade connection of electric element matrices into the
ABCD channel model. The impedance Z0 represents the load which is connected
to the output port, this last can be then switched between distinct values in order to
observe the variation of voltage in the input port of the global ABCD matrix.
63
Figure 3.11 Equivalent impedance diagram
Considering that the subscripts 1 stand for the voltage at the source, the
subscript i to the voltage at the input port of ABCD matrix, and the subscript 2 to
the output port of it, the the electrical-electrical equivalent matrix becomes
(97)
where the first matrix in the second term represent the electric matrix of the
series connection of a 50 Ω resistor the input port of the ABCD matrix, V1 and I1
are the voltage and current amplitudes of the voltage source, respectively and V2
and I2 are the voltage and current amplitudes at the impedance Z0 . These are related
by
(98)
The input and output ports of the ABCD matrix are related by.
(99)
One can observe that the input voltage Vi and current Ii are related to V1 and
I2 by the first equality in Eq. (99). Substituting V1 by 1 V and applying the
relationship of Eq. (98) leads to an expression that depends on the channel ABCD
matrix entries and the impedance Z0.
(100)
64
The input voltage, Vi changes when the impedance Z0 varies between two
values. It is worth mentioning that the analytical model solution is based on
frequency domain, and despite being possible to convert to time domain by
performing the inverse Fourier Transform, the result would be related with the
steady-state of the input voltage when varying the Z0 in two values. In other words,
it is not possible to evaluate the transient behavior. Nevertheless, the variation in
the frequency domain is carried out.
3.3 Models verification and comparison
This section evaluates both models in order to analyze their behavior when
varying some parameters and compare them as means of quantifying the capacity
of the system. The material properties of piezoelectric transducer, metal layer and
adhesive layer from table 3.4, in section 3.1.4 are used in the analytical and
numerical models. Thereby, power transfer is evaluated through the S21 parameter
following sections 3.1.5 and 3.2.5 for Pspice and analytical model, respectively.
Data communication capability is simulated in Pspice and analytically, evaluating
the input voltage in frequency and time domain following the sections 3.1.6 and
3.2.6, respectively.
The first simulation concerns an acoustic channel composed by Aluminum
and adhesive layers. Different thickness of the Aluminum layer were analyzed to
observe how the power pass through the acoustic channel, the adhesive thickness is
fixed at 100um. Fig. 3.12 shows the S21 values obtained with the Pspice and
analytical models, in which continuous line stand so analytical models and dotted
lines for Pspice model.
65
Figure 3.12 Power transfer analysis of both models varying the metal thickness
Fig 3.12 shows a characteristic pattern of an acoustic channel, simulated by
both models. The curves show multiple points of resonance and anti-resonance that
are related with a multipath propagation. Multipath propagation makes the signal
that reach the inside transducer dependent on the phase speed and thickness each
layer. One can also notice that increasing the thickness decreases the spacing
between the peaks. Since the goal is to transfer the highest quantity of power, the
most relevant parameter to evaluate is the frequency which has the highest peak. As
demonstrated in the Fig. 3.12 at about 2.27MHz, which is the transducer
fundamental resonance, a 5mm metal thick has an insertion loss, defined as the loss
of power when the wave travels a device, higher than of 10 mm and 15 mm thick.
It is naturally expected that the longer the metal later is the higher the insertion loss
would be since losses addressed in section 3.1.3 and 3.2.4 are dependent on the
layer thickness. This is however not observed. The reason for that is that due to the
distinct peaks distribution along the frequency spectrum. In the case of 5mm
thickness an anti-resonance valley coincides with the transducer fundamental
resonance frequency, considerably reducing the S21 at this frequency. Similar
behavior can happen for different material, due to the difference on the phase speed.
This behavior suggests that attention should be drawn since the peak of power
transfer may not present a monotonic relationship with the thickness of the layer.
The model are thus very useful to design a channel.
The highest value of power efficiency occurs for a 10 mm thick channel, it
has 0.56dB of insertion loss at 2.27MHz in Pspice and 2.33dB at 2.30MHz in the
66
analytical model. The maximum power transfer i s slightly out of the PZT
fundamental resonance frequency mainly because of the attachment of the
transducer on the metal , and the resonances distribution in frequency.
A second simulation with a fixed aluminum thickness of 13 mm and distinct
values of adhesive thickness is made, in order to evaluate the impact on power
transfer distribution when varying the adhesive thickness. Fig. 3.13 shows Pspice
and analytical results for this simulation.
Figure 3.13 Power transfer analysis varying the adhesive thickness
The frequency distribution reveals a dependence of the power with the
adhesive as the thickness increases. Distinct from the previously analysis, the S21
shape along the spectrum of frequency is more well-behaved, showing increasing
attenuation for increasing adhesive thickness from 50um to 150um both for Pspice
and analytical models. Therefore one can suggest that the adhesive thickness has to
be as lower as possible to acquire a good power transfer.
A third simulation is performed to evaluate the communication between the
PZT’s transducers. The simulation is performed by setting a 13mm of metal
thickness and 100um of adhesive thickness. Selecting the best point to operate
means to have the biggest difference in voltage on the outside transducer when
switching the electrodes of the inside transducer between two states or changing the
electric resistance in its terminals. In Pspice and analytical, a frequency domain
analysis is made, where the voltage on the outside transducer can be monitored
switching the inside electrodes between two different resistors 50 Ω and 0.22 Ω.
Fig. 3.14 show the amplitude on the outside transducer for the load values on the
67
inside transducer. Fig. 3.15 shows the difference of amplitude when the electrodes
of inside transducer is connected to two different values of resistor.
Figure 3.14 Input voltage V11 Pspice and analytical
Figure 3.15 V11 difference, 50 Ω and 0.22Ω in Pspice and analytical
As can be seen in Fig. 3.15 the acoustic channel is highly selective also in
amplitude voltages. The optimal frequencies of operation is found at 2.256MHz,
for the Pspice simulation, in which the V11 difference is about 0.4V. However at
the nearby frequency of 2.235 MHz the acoustic channel gives a variation of
approximately 0 V.
68
The frequency of 2.256MHz used in the Pspice transient analysis is showed
in Fig. 3.16. This operating frequency is the optimal value of this system and was
taken from the highest peak of Fig. 3.15. By swi tching S1 and S2 one can simulate
a binary digital communicat ion in Pspice. The transient analysis was not
implemented analytical ly as previously discussed in section 3.2.6. Figure 3.16
shows the signal in the time domain, the interval from 0 to 100μs represents the
period in which the switch S1 is closed and S2 is open, which means that a
resistance of 50 Ω is connected at the inside, and the interval from 100μs to 200μs
represents the period in which the swi tch S1 is open and S2 is closed, means that a
resistance of 0.22 Ω is connected at the inside.
Figure 3.16 Output PZT voltage at 2.256 MHz
In order to illustrate the high selectivity of the channel, the same switching
scheme is performed at 2.235 MHz, which according to Fig. 3.15 shows lower
variation. The result is shown in Fig. 3.17. As it can be seem it is almost unfeasible
to demodulate this signal
Figure 3.17 Output PZT voltage at 2.235 MHz
One can conclude that for both Pspice and the analyt ical models of PDAC system,
69
the shape of S21 parameter, with highly select ive peaks and valleys are nearly
coincident. This suggests that both models, although of different approaches, can
simulate acoustic channel and piezoelect ric behavior of the PDAC. Nevertheless,
the values of the peaks and val leys have slightly difference when comparing Pspice
and analytical model, this is mainly because of the different loss implementation in
each simulation. The Pspice model has four types of loss, two in piezoelectric
transducer and two in intermediate layer but none of them are frequency dependent.
The analytical model , on the other hand, has five types of loss, three in piezoelect ric
transducer and two in intermediate layer, where the di ffraction attenuation is
frequency dependent.
The transient results reveal the high difference of amplitude voltage in the
output PZT when the system is operating with two distinct frequencies. Using a
frequency of 2.256 MHz the amplitude varies 0.4 V but at 2.235MHz the amplitude
has a minor variation, showing that the system is highly selectivity.
In the next chapter evaluation and comparison between both models and
between experimental tests are performed, in which models use the same scenario
of the experimental setup, comprising metal and adhesive layers. In Pspice a more
complete circuit is connected on the acoustic channel, developed in this chapter, in
order to simulate the power and data transfer. The full circuit is capable of
simulating a digital modulation and demodulation, and powering all the inside
block electronics.
4 PDAC implementation
In chapter 3, an equivalent circuit for the acoustic channel with mechanical-
to-electrical analogy was developed. Designing the circuit in PSPICE allows one to
evaluate the power and data communication transfer and to perform transient
analysis. The overall circuit diagram (see Fig 3.1) illustrates the main elements
coupled to the acoustic channel block; namely, signal generator, RF amplifier,
envelope detector, voltage comparator, Mosfet transistor switch, energy harvesting
circuitry, microcontroller and sensors. These elements, either in the outside or
inside block, are necessary to provide power to the whole system and to modulate
and demodulate the sensors data. Most of these elements can be approximately
simulated in PSPICE by means of similar functions.
The type of modulat ion adopted in this work was Amplitude-shift keying (ASK).
In the next sect ions an introduct ion to ASK modulation is presented as well as the
developed electronics. The full system circuit and all the necessary elements to
modulate and demodulate the sensor data are described. The concepts of the mainly
elements of both, outside and inside blocks are also presented.
4.1 ASK
ASK belongs to the group of digital modulation. It is composed by a carrier
signal, a modulating signal and a modulated signal. The diagram of Fig. 4.1
illustrates these three signals. Distinctly from analog modulation in which the
carrier signal is modulated by a continuous signal, in the digital modulation a
discrete signal is used for modulating. Therefore, the carrier can be, for example,
modulated straightly from digital sensors data. The modulating signal is multiplied
by the carrier signal generating the modulated signal, Generally, in practice the
carrier frequency is a sinusoid wave with a frequency higher than the data baud rate
to avert the noise interference [101].
71
Figure 4.1 ASK modulation diagram
The modulating signal, or the sensor data information, is reconstructed using
an envelope detector circuit followed by a voltage comparator when the modulated
signals goes through the acoustic channel. One advantage in the use of a carrier
instead of simply transmitting the data in base band is that it can be generated in the
outside block, where there is no power restriction. The ASK demodulation has the
ability to be simple but efficient for low data rates, with few components the
modulating signal can be reconstruct in the other side of the channel.
4.2 Outside block circuit
The outside block has four main elements, namely signal generator, RF
amplifier, envelope detector and voltage comparator. The signal generator is
responsible for creating the carrier signal which is introduced into the acoustic
channel. The carrier frequency is to be previously selected from the AC analysis,
as presented in chapter 3.
Communication between the sensors, located in the inside block, and the
outside block relies on an amplitude modulation scheme, more precisely a digital
amplitude modulation (ASK), presented in section 4.1. Envelope detector and
voltage comparator are then necessary to implement the ASK demodulation
circuitry.
The circui t in Fig. 4.2 il lustrates the envelope detector implementation, which
consists of a diode and a resistor-capaci tor, RC low pass filter. The circui t operation
is as follows. Fi rstly, consider the posit ive half-cycle of the modulated signal. At
this stage the diode is forward-biased and the capacitor i s charging at the same rate
of the semi-cycle, if this is an ideal diode the stored voltage in the capacitor is the
peak value of the modulated signal. When the modulated signal decreases to a
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negative level, the diode becomes reversed-biased and the capaci tor discharges
through the resistor unti l the next positive cycle. Assuming this behavior, the RC
filter must be designed to have a time constant lower than the inverse of the
modulated signal bandwidth and greater than the inverse of the carrier signal
frequency [101], i .e.,
(101)
where fc and W are the carrier frequency and the bandwidth, respectively. According
to Eq. (101), resistor (R) and capacitor (C) of the RC filter, can be chosen to
properly demodulate the sensor signal.
Figure 4.2 Envelope detector schematic
The Fig. 4.3 shows an example of an ASK modulated signal with a carrier
frequency operating at 3Mhz and the envelope signal as a simple digital signal with
150kHz. The black line stands for the envelope signals and the red line to the
modulated signal.
Figure 4.3 Envelope Signal and Modulated signal example
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One can observe that only the positive half-cycle of the modulated signal is
demodulated and a lower peak voltage, Vpeak, is reached as the envelope detector
has a non-ideal diode. The peak value, which originally is 1V, after the diode drops
to 0.8V, approximately. It is also noticeable the charge and discharge of the
capacitor on the resistor. This rate is determined by the values of the RC filter.
Decreasing the constant time directly impacts the time to reach the high logical
level, whereas increasing it affects the low logical level. The chosen RC values for
this example gave a high level of 0.6V, black flag in Fig. 4.3 and a low level of 0V
with a high to low transient time of 2us.
As it can be seen, the envelope detector provides the amplitude variation
which is related to some information, for instance from a sensors whose output data
is used to modulate the carrier at the input port.
Since the acoustic communication of the system is digital, as the sensor data
is digitized, the envelope signal is connected to a voltage comparator that
reconstructs the digital information of the sensors. A simple voltage comparator can
be made using an operational amplifier [102], illustrated in Fig. 4.4. This
component works with two inputs one being a reference voltage and the other the
signal to be compared, in this case the envelope signal. When the envelope signal,
is greater than the reference voltage, the output of voltage comparator is high (V+),
when the envelope signal voltage is lower than the reference voltage, the
comparator output signal is low (V-).
Figure 4.4 Voltage comparator diagram
Passing the envelope signal through the voltage comparator results in a digital
signal in the output port. Ideally, the output signal is 5V when the original datum is
in logical level high and approximately 0V when it is in low. These levels depend
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on the supply voltage of the operational amplifier. This functionality turns the
voltage comparator into a digital converter.
Fig. 4.5 illust rates the envelope signal, the threshold level, the comparator
output signal and the modulating signal. In this example the reference voltage is
0.5V, which is the voltage that the envelope signal changes from logical level .
Figure 4.5 input and output signals of the voltage comparator
The comparator signal has 500ns of difference from the modulating signal
when the logical level changes from high to low, this fact is caused by the voltage
reference chosen and the time response of the voltage comparator. This difference
directly impacts the maximum data rate for a given carrier signal.
Therefore, the outside block is not only responsible to supply power to the
outside PZT transducer and, consequently, to the inside block, but also to recover
the modulated data from the sensors located in the inside block.
4.3 Inside block circuit
The inside block is designed to work passively, i.e. it operates without any
conventional power source. The power that supplies the sensors and microcontroller
comes from the electrical signal at the inside PZT transducer terminals. This
electrical signal comes from the acoustical (mechanical) waves that impinge the
transducer face and are then converted to voltage difference between its terminals.
To transform the AC signal received in the terminals of the PZT transducer
into a DC source capable of supplying energy to all other elements in the inside
block, a voltage doubler circuit is adopted [103]. The topology used is showed in
Fig. 4.6.
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Figure 4.6 Voltage doubler topology
With two schottky diode-capacitor pairs the fundamental operation of the
circuit is to multiply and rectify the input AC voltage to give a DC output. In other
words, the peak voltage of the RF carrier is multiplied by a factor of two using the
topology of Fig. 4.6. Taking into account the voltage drop of both diodes, the output
Vdc is,
(102)
where Vpeak is the AC signal on the inside PZT and Vfdiode is the diode forward drop
voltage.
The output Vdc has a voltage that can vary depending on the PDAC
environment and for this reason a voltage regulator is introduced to hold the output
voltage constant, regardless the value of the obtained Vdc. The components in the
inside block (sensors, microcontrollers and other IC’s) can have different ranges of
input supply voltage and therefore mult iples voltage regulator with different output
voltage can be used, such as 3.3V and 5V.
The inside block transmits the sensors’ data to the outside block by switching
the inside PZT terminals between two states, open and short-circuited. To perform
this procedure a MOSFET transistor with a low resistance of conduction must be
used. That is, when it is switched on, a minimum series resistance between the
terminals of PZT is achieved, approaching an ideal short circuit.
In Fig. 4.7, the RF carrier signal obtained at the inside PZT is connected in
parallel with the MOSFET. The digital sensor data turns the MOSFET “on” and
“off” as the high and low voltage levels reaches the gate port of MOSFET,
respectively.
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Figure 4.7 Mosfet switching RF carrier
4.4 Full system simulations
It is possible to simulate the PDAC with the peripherals circuits of outside
and inside blocks. Using a PSPICE simulator the circui t is designed as shown in
Fig. 4.8. The PDAC system has exactly the same characteristics presented in the
chapter 3 and the materials which compose the acoustic channel have the properties
of table 3.3 with 10mm of aluminum thickness and 100um of adhesive thickness.
In the ci rcuit simulat ion, the output block, black rectangle in Fig. 4.8, is
formed by a simple AC source operat ing at 2.25MHz, which produces the highest
variation in ampl itude for the Pspice simulation, see sect ion 3. 3. The AC source has
30Vp and a 50 Ω output impedance simulating the output of a RF ampl ifier.
Additionally to the presented envelope detector in section 4.2, here others
components were included to ensure the proper funct ional ity of the ASK
demodulat ion, for instance, a low pass fil ter and a DC blocker.
In the inside block, red rectangle in Fig. 4.8 the voltage doubler has two schot tky
diodes and two capacitors where C1 and C2 are chosen to optimize the power
transfer. T he 5V vol tage regulator used is the LT1117-5 from Linear Technology®
[104]. The MOSFET transistor has an extremely low resistance, 0.22Ω when
conducting, given the sufficient path to ground.
The digital output part of circuit, light green rectangle in Fig. 4. 8 simulates
the microcontroller and sensors. Its power consumption is approximately 150 mW
when driving the MOSFET and the data rate is 10 kHz in cont inuous mode.
4.5 Full system simulation results
In this section, the results obtained from PSpice simulation of both,
modulation and demodulation circuits and the acoustic channel are presented.
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Figure 4.8 PDAC full system with electronic peripherals circuits
78
Some critical signals from the circuit are illustrated below to validate the use
of the electronic components associated with the outside and inside blocks.
4.5.1 Outside block simulation
The outside block is the black rectangle in Fig. 4.8. One of the most
important signals of the outside block is the modulated signal connected between
the 50Ω impedance of the signal generator output and the electrical port of the
output PZT; the electric node of this is signal marked with number (1) in Fig. 4.8.
This signal is illustrated in Fig. 4.9.
Figure 4.9 Modulated signal of full system
The modulation produced by the digital output gives a 3.75V between high
and low voltage levels operat ing at 2.256MHz. The modulated signal passes
through the envelope detector circuit reconst ructing the sensor data information,
number (2) in Fig. 4.8. The demodulated signal output, biased to 2.5V, can be seen
in the Fig. 4.10.
Figure 4.10 Sensor signal of full system
2.5V
79
Comparing Fig. 4.9 and 4.10 one can see that the peak-to-peak voltage of the
recovery signal is 0.55V (=3.75V-3.20V) lower than the difference from the high
to low values of the modulated signal. This lower voltage is due to the diode voltage
drop and the low pass filter attenuation, necessary elements for the operation of the
envelope detector. One can also notice that the first levels are not stabilized, this is
due to circuit and acoustic time responses.
Following the circuit, there is the voltage comparator signal, number (3) in
Fig. 4.8. As presented in section 4.2, it transforms the sensor signal into a digital
signal with two voltage levels, namely 0.2V and 5V. The signals is commuted
between these levels at exactly the same data rate of the sensor. This signal is shown
in Fig. 4.11,
Figure 4.11 Comparision between sensor information and comparator signal
The reference voltage is fixed in 2.5V due to the voltage divider composed
by the R7 and R9 elements of Fig. 4.7. This level is chosen because it lies at about
the middle of the maximum and minimum level of the sensor signal The comparator
signal turns the sensor signal of Fig. 4.8 into square pulses with the same data rate,
reconstructing the digital information of the sensors.
4.5.2 Inside block simulation
In the inside block some useful signals can be collected to show the
functionality of the PDAC and the inside electronic peripherals. In Fig. 4.8, a digital
pulser simulates the consumption and data transmission of the sensors and
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microcontroller of PDAC. (this is illustrated by the rectangle in lime color). The
digital pulser is only turned on , by the swi tch SW in Fig. 4.8, when 4. 6V levels is
reached in the output port of the voltage regulator; this provides the proper time to
the system to stabilize i tself before starting the communication. In pract ice this
element i s not present in the real circuit , but for the purpose of Pspice simulation it
helps the stabil ization and convergence of the simulation.
The Fig. 4.11 shows the sensor information that i s transmitted from the inside
block to the outside block, number (6) in Fig. 4. 8, in red line. The output of the
digital pulser is connected to a BJT transistor that inverts the digi tal signal and
drives the MOSFET, which in turn shorts or opens ci rcuit the inside PZT to ground,
respectively. Aiming to compare the signal received in the outside block, the
comparator signal i s also illust rated in Fig.4.11 in black line.
One can notice that when comparing the sensor informat ion with the output
of the comparator, the signals are shifted in time. This delay, approximately of
5.2us, is associated with the wave propagation ti me inside the aluminum, speed of
6420 m/s and thickness of 10mm, accounting 1.6 us, the delay of the envelope and
low pass filter and the delay of the vol tage comparator. As the waves pass through
a physical medium there is a time for them to propagate through the layers
(according to the sound speed in each material ), causing a shift in t ime.
The voltage at the inside PZT electrodes (number (4) in Figure 7) is shown
in, Figure 4.12,
Figure 4.12 Inside PZT signal
The amplitude of the inside PZT gets null when the digital pulser of Fig.4.9
is in low level, activating the MOSFET. The process is reverted when the digital
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pulser is in high level, deactivating the MOSFET. The inside PZT signal in this
stage has a Vp of approximately 12V. One can also notice the signal stabilizing
after some periods since the system has been switched on. Other characteristics is
the suppression of the negative part of the signal when the MOSFET switch is
deactivated. This is caused due to the MOSFET intrinsic diode between drain and
source when in off state.
As the inside PZT has a voltage drop every t ime the sensor data i s in low state, it is
not possible to supply power to the system without the use of a recti fier circuit and
a voltage regulator.
Fig. 4.13 shows the behavior of the output voltage, number (5) in Fig. 9.
Whi le the steady state is not achieved the output voltage increases until , some
periods have passed and then a 5V vol tage source, recti fied and filtered is
established. T he abscissa scale of figure 4. 13 is exactly the same of figure 4.12.
Figure 4.13 5V voltage regulator output
4.6 Experimental setup
Up to this point, the dissertation has presented two models, one numerical and
the other analytical. The former uses the analogy between electrical and mechanical
to create an equivalent electrical circuit that can be simulated using circuit
simulation software, for instance Pspice. The latter is based on 2-port ABCD matrix
with the intermediate layer being modeled by the wave propagation equation and
the piezoelectric layer modeled by the constitutive piezoelectric equations.
82
Experimentally, the power transfer analysis is assessed using a Vector
Network Analyzer (VNA). This equipment is capable of measuring the transmitted
signals between two ports and the reflected signal of an individual port. The VNA
used in the experimental part is E5061B from Keysight® which operates from 5Hz
to 3GHz. The parameters that quantify the transmited (S21) or reflected (S11)
power used by the VNA were previously discussed in the section 3.1.5. The S-
parameters give the necessary information to evaluate the power transfer of
experimental system.
The data communication analysis also uses the VNA, however an impedance
analysis is performed to extract the voltage difference in the output PZT when
switching the inside PZT. Thus, it is possible to evaluate the operational frequency
that has the major difference in amplitude and consequently a better data
communication point. After that, an analysis using the oscilloscope and a signal
generator allows the evaluation of a transient characteristics of the PDAC, in this
configuration, i.e. a fixed frequency is set and the inside PZT switched by a Mosfet
transistor.
This section is divided in two experiments. The first consists of a flat plate
sandwiched by two PZT transducer. The other by a layer of water and a curved
surface made of metal (which actual ly is a pipe wall) in the middle of two PZT
transducers.
4.6.1 Flat plate
This section describes the experimental approach designed to validate the
analytical and numerical analysis presented in chapter 3. T he first experiment
consists of a flat plate made of Aluminum with 13mm and a pair of PZT4
transducers from PICeramic® [105] operating at 2MHz. The PZT transducers and
the Aluminum plate were bonded together with an Araldite epoxy adhesive from
Hunstaman® [106] in such way that the transducers are co-aligned. Transducer
bonding position was determined by previously measuring, with a ruler, and
marking the desired position for the center of each transducer on the plate’s
surfaces.
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In this experimental setup the thickness of the adhesive layer, after the cure
process, was measured in 150um, using a micrometer. T he PZT4 transducer has a
nominal resonance frequency of 2MHz given by the manufacturer and a thickness
of 1. 00mm, measured using a micrometer. The Aluminium thickness is 13.05mm,
also measured using a micrometer. The properties of the PZT can be found in the
PI Ceramic material datasheet however [113], a characterization is made using the
VNA, a micrometer and a scale.
The method of characterization follows the following steps:
• Measurement of the resonance and anti-resonance frequencies,
• Measurement of the capacitance in 1kHz3,
• Measurement of the impedance value at the resonance peak,
• Measurement of the thickness and area of PZT transducers.
After this procedure a list of parameters is calculated as mechanical quality (Qm),
elastic stiffness (CD
33), thickness electromechanical coupling constant (kt), wave
velocity (v), permittivity (ε33) and piezoelectric pressure constant (h33). The density
(ρ) was measured using the micrometer and a scale. The equations to calculate these
parameters are located in [107].
The Aluminum plate and the adhesive were characterized using a pulse-echo
method to acquire the speed of sound and the viscous attenuation. The data of the
pulses were measured using an oscilloscope (Tektronix® DPO4054) and the pulse
was generated and pre-amplified with The Pulse-Receiver (Olympus® 5072PR).
The table 4.1 summarizes the parameters experimentally acquired. All the
parameters were measured unless otherwise stated.
3 Since the PZT is mostly capacitive in low frequency, the capacitance determination is
measured in 1kHz.
84
Table 4.1 Material properties
Piezoelectric
Property (units) PZT4 (PiCeramics)
ρ (kg/m³) 7641
υ (m/s) 4525
Qm 1500
ε33s / ε0 716
κ33 0.52
C33 (N/m²) 16.04x1010
A (m²) 386x10-4
Adhesive
Property (units) Epoxy (Hunstmann)
ρ (kg/m³) 1400
υ (m/s) 2344
αv (Np/m)4 172
A (m²) 386x10-4
Metal
Property (units) Aluminum
ρ (kg/m³) 2791
υ (m/s) 6291
αv (Np/m)5 0.46
A (m²) 386x10-4
Fig. 4.14 shows the impedance curve from 1 to 4 MHz of the PZT4 transducer
for the two models, Pspice and analytical and experimentally acquired on VNA.
4 The viscous attenuation of the adhesive was acquired from Prada et. al.
5 The viscous attenuation of the Aluminum was acquired from [20]
85
Figure 4.14 Impedance curve for Pspice, Analytical and experimental
4.6.1.1 Flat plate power transfer analysis
A diagram illustrating the power transfer characterization of the flat plate and
the experimental characterization using VNA is showed in Fig. 4.15.
Fig. 4.16 compares the analytical, the Pspice simulated and the experimental
power transfer, data is acquired from 1MHz to 4MHz with 1601 points. The Pspice
maximum point is reached at 2.186 MHz with a insertion loss of 3.23dB. The
maximum frequency of the analytical model is extremely close at 2.188MHz,
however with 6.54dB of insertion loss, a considerable attenuation comparing to
PSPice. Finally, the experimental analysis is also at 2.188MHz and its insertion loss
is 5dB. Table 4.2 summarizes this values.
Figure 4.15 Schematic (a) and experimental (b) characterization of the flat plate
using VNA
86
Figure 4.16 Flat plate power analysis
Table 4.2 Power Transfer of Pspice, analytical and experimental
Power Transfer
Method Frequency of
maximum
(MHz)
Maximun
S21(dB)
Pspice 2.186 -3.23 Analytical 2.188 -6.54
Experimental 2.188 -5
The main difference between Pspice and analytical model is related to the
losses implemented in each model, as discussed in the chapter 3. When comparing
both models with the experiment, it is observed that the peaks of resonance
distributed in the frequency range match. It is also noted that the analytical model
has more consistency with the experiment. This suggests that the more strict losses
modeled in the analytical implementation are relevant for a more precise
characterization of the physical phenomenon.
4.6.1.2 Flat plate data communication analysis
As done to determine the S21 parameter, which is a function of frequency,
the communication is firstly analyzed in the frequency domain, as presented in
section 3.2.4. The diagram of figure 4.17 shows the setup made to acquire the
reflected impedance (Z11) in VNA using the impedance analyzer tool. In this
configuration only the port 1 of the VNA is used. The signal generator (ARB) varies
the load terminator of inside PZT into 50 Ω and an equivalent impedance of 0.22
87
Ω. Then the measured spectrum of Z11 is transformed to V11, which is the main
parameter to evaluate data communication. This signal is labeled by number (1) in
Fig. 4.8.
Figure 4.17 Setup for data communication analysis in frequency domai n
The relationship between the impedance and the voltage uses the principle of
voltage divider. Figure 4.18 illustrates a schematic of the equivalent circuit. Eq. 103
represent the conversion between Z11 and V11 when the output impedance of port
1 is set to 50 Ω and the amplitude of the voltage generator is 1Vpp.
(103)
Figure 4.18 Voltage divider theory
The Pspice directly gives the input voltage as it is a circuit simulator, however, the
analytical model has to be manipulated to transform the ABCD transfer function
into a voltage relationship and acquire the (V11), as explained in section 3.2.6.
Fig. 4.19 shows the input voltage (V11) for the two termination load levels,
for Pspice, analytical model and experiment. Fig. 4.20 illustrates the difference in
V11 between the two load levels. In both curves a zoom is made in the range that
contains the maximum difference in voltage amplitude.
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Figure 4.19 (a) Input voltage (V11) varying the termination load and zoom (b) between 2.1
and 2.5 MHz
Figure 4.20 Difference in amplitude voltage
In Pspice, the frequency that has the highest difference in V11 is located at
2.194MHz, which is 4 kHz shifted from the point of maximum power transfer. In
this frequency the voltage variation is 0.31V. For the analytical model the maximum
difference in V11 is 0.15V at 2.206 MHz The best frequency to communicate the
data is slightly distant from the highest point to transfer power in this model, having
a shift of 18 kHz. The experimental curve has the same pattern in Pspice and in the
89
analytical model. However, the analytical model is more precise in the differences
of V11, when compared to the experiment. This is probably due to the associated
losses which are frequency dependent, see section 3.2.4. The experiment presented
a peak of V11 difference of 0.19V at 2.188 MHz, which is totally coincident with
the point of maximum power transfer. Table 4.3 summarize the maximum voltage
difference.
Table 4.3 Highest difference in amplitude
Maximum voltage difference
Method Frequency (MHz) V11 difference (V)
Pspice 2.194 0.31 Analytical 2.206 0.15
Experimental 2.188 0.19
In the sequel, the flat plate is exposed to a time domain analysis that is based
on the diagram of Fig. 4.21. In this figure, the output signal with a constant
frequency is connected to the outside PZT. On the other side the inside PZT is
switched to ground with a MOSFET.
Figure 4.21 Setup to measure the input voltage (V11)
The resulting signal seen in the oscilloscope is shown in figure 4.22. The
signal generator amplitude was set to 1V at 2.188MHz. The variation of amplitude
considering the maximum and minimum amplitude of each period of the digital
pulser is approximately 0.16V. This figure also shows the signal obtained by Pspice
operating with 1V at 2.194MHz. About 0.3V of difference in amplitude between
high and low levels was obtained. Both values are coherent with the ones of table
4.3 and in both case the high level occur when the MOSFET is conducting and the
low level when the terminator is connected to a 50 Ω termination load. This analysis
90
was not performed with the analytical model because this is based only on
frequency domain with harmonic responses, as commented in section 3.2.6.
Figure 4.22 Input voltage signal flat plate experimental test
The result of 0.16V in amplitude difference makes the demodulation quite
challenging using the elements presented here, mainly because of the threshold
voltage noise of the comparator. However amplifying the signal 10 times, for
example, and considering a linear system, the amplitude difference could increase
also 10 times, keeping the threshold voltage noise constant and turning the
demodulation much easier
Analyzing the behavior of the signal it is possible to conclude that the
multipath propagation of PDAC turns the acoustic channel into a resonant system
when operating at a specific frequency. Consequently, the multiple propagating
waves create a standing wave inside the material. Every time the input PZT is
switched, a new standing wave has to be established. In practice, this phenomenon
can be observed in Fig. 4.22. Until the steady state is reached the signal has a time
response when varying between the two state levels.
91
4.6.2 Curved surface - Tube
A second experiment was carried out, it consists of two concentric tubes. One
tube is made of carbon steel and has 325 mm of external diameter and 6.5 mm of
thickness, the second is made of aluminum and has 220 mm of external diameter.
The space between the tubes was filled with water. The water layer has 67.8 mm.
The table 4.2 summarizes the properties of the additional materials used in this
second experiment. Properties that does not have the footnote were characterized
using the pulse-echo method, scale and micrometer.
Table 4.4 Material properties - Tube
Piezoelectric
Property (units) PZT4
(Ultraceram)
ρ (kg/m³)6 7900
υ (m/s) 4671
Qm 234
ε33s / ε0 889
κ33 0.57
C33 (N/m²) 17.2x1010
A (m²) 491x10-4
Metal
Property (units) Carbon Steel
ρ (kg/m³) 7715
υ (m/s) 5874
αv (Np/m) 0.8
A (m²) 491x10-4
Fluid
Property (units) Water (20°C)
ρ (kg/m³)7 1000
υ (m/s) 1484
αv (Np/m)8 0
A (m²) 491x10-4
6 Data taken from manufacture contact
7 http://www.ondacorp.com/images/Liquids.pdf
8 The viscous loss is 0.001 Np/m @ 400Khz in [108]
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The water layer is simulated as an intermediate layer in Pspice and analytical
models. The viscous loss of water is extremely low and for this reason it can be
considerate 0 Np/m [108] however, considering the thickness of intermediate layer
the spreading loss must be calculated. A three-dimensional sketch of this
experimental configuration can be seen in Fig. 4.23. For this experiment two PZT-
4 transducers with nominal frequency of 1MHz, 2mm of thickness, purchased from
UltraCeram®[109] is used. The external PZT is bonded on the external surface of
the tube with Hunstmann® 2015 epoxy. Before this, a recess is made on the curved
surface of the external tube leaving a plane surface area that facilitates the bonding.
Figure 4.23 Three-dimensional sketch of curved surface experiment
On the other hand, the internal PZT was attached with the aid of a structure
made on a 3D printer, model Replicator Z18 by MakerBot® and illustrated in Fig.
4.24. This structure allows the alignment between the internal PZT and the external
PZT and isolates the transducer back face from the water, (front face illustrated in
Fig. 4.24) this ensures that the transducer back layer is filled with air. The presence
of air on the transducer back layer is important so the waves on the back face of the
transducer does not interact with the materials in the back. An air layer introduces
a very poor coupling between the ceramics and the material due to the high
impedance mismatch between ceramic and air. Another purpose of the back layer
filled with air is to minimize the bandwidth of the transducer keeping the Q factor
as high as is possible [110].
93
Figure 4.24 3D CAD and Structure made on 3D printer to isolate the back face of transducer from water
4.6.2.1 Curved Surface power transfer analysis
As done for the flat plate experiment a comparison of the power transfer is
made between the two models and the tube experiment using VNA, which is
calibrated and set to realize measurements in the range of 800kHz to1.4MHz with
1601 points. The Fig 4.25 shows the three curves.
Figure 4.25 Power transfer analysis for curved surface experiment
One can notice the coincident peaks of resonance between the Pspice and
analytical model but slightly difference, approximately 4 kHz, when comparing
with the experimental. This can be caused by distinct characterized values of the
many necessary parameters, see table 4.4, and the one-dimensional model
implemented. Anyhow, the peak of transmission has 6.86dB at 1.040MHz of
insertion loss for Pspice model, 7.41dB for analytical model at 1.041MHz and 8.45
at 1.030MHz and 1.043MHz for experimental. Table 4.5 summarizes the insertion
loss in each case.
94
Table 4.5 Power transfer peak of curved surface experimental setup
Power Transfer peak
Method Frequency(MHz) S21(dB)
Pspice 1.040 -6.86 Analytical 1.041 -7.41
Experimental 1.030/1.043 -8.45
Similar to the flat plate case, the Pspice model has the resonance peaks with
low insertion loss for all the spectrum and the analytical more coincident with the
experimental, mainly for the range between 800kHz to 1.04 MHz.
4.6.2.2 Curved Surface data communication analysis
Following the power transfer analysis, the data communication analysis is
made in Pspice, for the analytical model as well as for the experiment setup, setting
the range of analysis to 800kHz to 1.4MHz with 1601 points, Figure 4.26 shows the
curve of the input voltage (V11) for Pspice, analytical and experiment varying the
load termination between 50 Ω and 0.22 Ω.
Figure 4.26 Input voltage (V11) – curved surface
The difference between these three curves of amplitude is best seen in the
Fig. 4.27. The figure shows the range 995kHz to 1.05MHz. Although, the analysis
of power transfer shows that the Pspice and analytical model are very similar, the
analysis of the input voltage shows differently. One can notice in Fig. 4.27 that the
amplitude of the analytical model is closer to the experimental data.
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Figure 4.27 Input voltage between 0.95MHz and 1.05MHz – curved surface
It is possible to notice from Fig. 4.27 that in Pspice the frequency which has
the maximum difference in voltage (1.030MHz) is considerable different from the
maximum power transfer (1.040MHz), however a second peak with high amplitude
is located at 1.040MHz. The analytical model also has a difference between the
maximum power transfer (1.041MHz) and the maximum difference in voltage
(1.008MHz) but also has a high peak at 1.041MHz. The experimental, otherwise,
has the two major peaks, with almost the same level, which are coincident for the
maximum power transfer and difference in voltage (1.030MHz and 1.043MHz).
Table 4.6 summarizes the results of V11 difference for the Fig. 4.27.
Table 4.6 Voltage difference of the input voltage
Maximum voltage difference
Method Frequency
(MHz) V11 difference
(V)
Pspice 1.030 0.1629 Analytical 1.0081 0.17
Experimental 1.030/1.043 0.07
Comparing this resul t with that the one shown in Fig. 19b, it i s observable an
increase in the number of peaks since this experiment has a water layer wi th high
thickness (74.32 mm instead of 13. 08 mm). The system with a higher thickness and
lower veloci ty has higher selectivity in frequency. This selectivity also known as
cyclic frequencies [7] happens when a standing wave is formed in the layers of the
acoustic channel and it i s governed by the Eq (104).
96
(104)
Where cm is the metal sound velocity and l is the thickness of metal [7].
Nevertheless, the difference in voltage (V11) is proportional to the losses and
the matching between the acoustic impedances of the materials. With higher
thickness and more layers, the difference in V11 has lower voltages when
comparing with the flat plate experiment, however with a higher thickness and/or
lower velocity the system increases the amount of standing waves per frequency
interval formed inside the layers and more frequencies appear as candidates to be
used. One can also notice that the values of the difference in V11 illustrated in Fig.
4.29 has almost the same peaks amplitude for this range.
Figure 4.28 Input voltage difference between 50 and 0.22 ohms, full frequency range
Figure 4.29 Input voltage zoom for frequencies between 1 MHz and 1.05 MHz
97
Comparing the frequency in which the maximum difference in V11 (Table
4.6 and 4.3, respectively) and the maximum power transfer (Table 4.5 and 4.2,
respectively) occur for both, in flat plate and curved surface cases, it reveals a small
and medium differences between these frequency points in Pspice and analytical
models, respectively. Nevertheless, the experimental results shows that for both,
flat plate and curved surface, the frequency that has the maximum difference in V11
and power transfer are coincident.
Fig. 4.30 represents the transient analysis of V11 for experimental and Pspice
model. In this analysis the frequency of the signal generator is set to operate at
1.040Mhz with a output of 10V, for both experimental and Pspice simulation . The
same frequency is used for Pspice transient analysis simulation. The maximum
difference in voltage for Pspice is 1.5V and 0.6V for the experimental setup. At this
frequency the values have approximately the same values of the frequency domain
analysis illustrated in Fig. 4.29 and summarized in Table 6.
Figure 4.30 Input voltage transient analysis - Curved surface
4.6.3 Full system experimental analysis - Tube
In this section, a full system interrogation with the same configuration of
figure 4.9 is detailed using a P&T sensor connected to the inside module. This full
system is assessed in the Curved Surface configuration (section 4.6.2). For the sake
of clarity a concise recall of its main blocks is shows in Figure. 4.31.
98
Figure 4.31 Schematic diagram of the curved surface experiment test
As one can see, a fixed frequency is generated by a RF signal generator
(label 1.1 in Fig.4.31) and them amplified by an RF amplifier (label 1.2 in Fig.4.31).
The outside modules responsible to send the amplified signal to outside PZT
transducer (label 1.13 in Fig.4.31) and to send the demodulated sensor data to a
personal computer (label 1.14 in Fig.4.31). In this setup the outside block presents
the following equipment’s: signal generator Tektronix TSG 4104A®[114], (label
1.6 in Fig 4.31), power amplifier E&I® model 2100L [115], (label 1.2 in Fig 4.31),
and DC source Keythley® model 2220-30-1 [116] , (label 1.3 in Fig 4.31). In the
inside block, the P&T sensor is based on MEMS technology from OpenField®
[117], (label 1.9 in Fig 4.31), the microcontroller, MSP430 architecture [118] ,
(label 1.8 in Fig 4.31), has low power feature to ensure the proper functionality of
the system since the inside block receives a limited power from the outside block.
The metal, PZTs and the adhesive are the same listed on the section 4.6.1. The
experimental bench of the full system is shown in the picture of figure 4.32. The
inside and outside block circuits are in metal boxes to minimize the influence of
electromagnetic interference. The sensor’s data are displayed on the monitor of the
PC. The first column is the pressure in (psi) and the second the temperature in (°C).
All the cables have 50 Ω of impedance.
99
Figure 4.32 Full system experimental bench
Figure 4.33 shows the V11 signal in purple and the sensor information in
green, read at the output of the power amplifier, label number (2.1) and at the
microcontroller output, label number (2.3) in Fig 4.31, respectively, when the full
system is operating. As it can be seen, the high level (1) and the low level (0) of the
sensor information has the same “bit” duration of V11 signal, purple signal. The
operational frequency is fixed in 1.043Mhz, which provided the best difference in
voltage, see section 4.6.2.2, the amplifier output is set to 10W (40dBm) providing
approximately 1.4W (31.5dBm) to the inside block, that is, the loss is 8.5dB which
is the same obtained in section 4.6.2.1.
100
Figure 4.33 Sensor information signal in green and the input voltage signal on the outside
block in purple
Table 4.7 Power consumption of the main elements in the inside block
Inside Block Consumption
Element Power(mW)
Microcontroller 3.3
Sensor 16
Driver 115
The communication between the microcontrol ler and the sensor is made
using synchronous I²C protocol [111], the sensor is interrogated at a rate of 1Hz.
The pressure and temperature values of the sensor are converted to ASCII before
transmit ting the information to the outside block using UART. The microcontroller,
on the other hand, switches the MOSFET through a bipolar transistor, highlighted
by dark green rectangle in Fig. 4.8, as the microcontroller output port can drive a s
the signal up to 4mA. A diagram, Fig. 4. 34, is shown to clari fy the sensor-
microcontroller communicat ion and switch is operation.
101
Figure 4.34 Block diagram of protocols used in the inside block
Since UART protocol stays idle with high level (3.3V), the (BJT) driver is
configured to invert the digital information of the sensor, switching the 1’s by 0’s
and vice-versa. Thus, the MOSFET does not short- circuit the inside PZT terminals
when not transmitting the information.
The input voltage V11 signal passes to the envelope detector, label number (2) in
Fig. 4.8, and then to the voltage comparator, label number (3) in Fig 4.9. The output
signal, after passing through this two elements is shown in Fig. 4. 35 where the
purple signal is the demodulated signal and the green the sensor informat ion. One
can notice the shift in time between both signals that occur due to wave propagat ion,
as commented in section 4.5.2.
Figure 4.35 Sensor information signal in green and purple the signal after the voltage
comparator in purple
The output of the voltage comparator is connected to a computer by using an
UART-to-USB converter from FTDI®[119], label number (1.5) in Fig 4.31. Since
the sensor’s data is in ASCII format, the temperature and pressure values are
102
directly displayed in any terminal software opening a virtual COM port, as shown
in figure 4.32.
The sensor data passing through the acoustic channel and directed connect to
microcontroller is then compared, as shown by flags, label number (2.2) and (2.3),
respectively, in Fig 4.31, both of them are connected to an UART-to-USB converter
before displaying in terminal on PC, as shown by labels (1.5) and (1.11),
respectively. Figure 4.36 shows the two curves of temperature acquired in time. The
red line stands for the raw sensor data, which is the sensor information in the inside
block, black line stands for the demodulated sensor data, and which is the sensor
information passing through the acoustic channel on the outside block.
Figure 4.36 Comparison between raw and demodulated temperature sensor data
The sensor is exposed to temperatures varying from 40°C to 60°C inside a
chamber model 400-TD from EthikTechnology® [120], label number (1.10) in Fig.
4.31. In this test when the system is in the beginning of operation, until the instant
represented by the blue arrow in Fig.4.36, the demodulated sensor data reconstruct
the information without any errors (one can see that black and red line coincide in
the very first instants). However, at approximately two minutes later, the amplitude
of the signal after the envelope detector, label number (2), in Fig. 4.8 starts to
decrease and the reference (threshold level) of the comparator is out of the high and
low levels of the envelope signal. This implies in, errors in the measurement that is
interpreted as 0°C, this instant is indicated by a blue arrow in Fig. 36. After
manually adjusting the threshold level the system operates without errors for
approximately three hours and twenty minutes (black and red line coincide),
without the need of any more none readjustments. The raw sensor data and the
demodulated sensor data in this period measured the same values of the sensor.
103
At the time marked by the green arrow, 3h and 25m, in figure 4.36, the
demodulated sensor starts to provide wrong data. Since no further adjustments was
made, the data still in 0°C during the rest of the test, orange rectangle in Fig. 4.36.
However, the raw measurement still receiving data from the sensor, which means
that the inside block is fully operating at this stage and has sufficient power to
supply the electronics peripherals.
The main causes for the non-correct demodulation of the signal, both in the
beginning of the experiment (blue arrow) as well as in its end (green arrow), can be
associated with two main parameters observed in the experiment. The first is a
slightly shift on the frequency in which the highest V11 difference occurs. This was
observed by monitoring the V11 difference along the time. One cause of this
phenomenon is, probably caused by the variation of temperature, which affect
solids[121] and liquids [122]. This causes a change on the levels of the envelope
signal, which eventually drift it to out of the threshold level. The second is a
phenomenon similar to cavitation [123] that generates bubbles in the water , with a
mid-power (10W) operation this phenomenon becomes present after some time,
and the waves behaves with high instability, impairing the behavior of the system.
The Fig.4.37 shows a picture with the bubbles inside the water, formed because of
the cavitation-like phenomenon.
Figure 4.37 Bubbles generated inside the water due to cavitation -l ike phenomenon
As demonstrated by this experiment, using sufficient power on the outside
block to supply energy for the inside block and by properly adjusting the threshold
level on the voltage comparator, the system is capable to power all inside block and
sensor and to demodulate the sensor information successfully. A critical point of
this system is the proper adjustment of the comparator threshold level. In this
experiment adjustment was done manually. A natural evolution of the present
system is to count on an automatic self-adjusting logic unit to search for an
optimum frequency.
5 Conclusion
Analytical and numerical models were evaluated and extended. Simulation
showed that the thickness of the adhesive and metal layer impacts on the power
transfer efficiency. Increasing the thickness of the adhesive also increases the power
loss. On the other hand, increasing the thickness of metal not necessarily increases
the power loss, due to the resonances distribution in frequency. The search for the
proper channel configuration is thus important and the models aid in this task.
Communication was assessed by simulating the input voltage (V11) of the
system. The evaluation of data capacity was adopted in the frequency and time
domains. The amplitude modulation of the input voltage, in transient response,
shows a coherent behavior compared to the frequency response, and also shows the
high selectivity of the channel when slightly varying the operating frequency.
When comparing the experiments with the two models used, the power
transfer showed a coherent result with a great proximity in the peaks of resonance
and anti-resonance. However this agreement was not clear in the communication
analysis mainly in the curved wall-water configuration. Data communication
analysis is affected by the complex impedance of the system. Pspice and analytical
model have particular losses in their models, implying a different real and
imaginary part of the equivalent impedance (Z11). A slightly shift of the peaks in
the V11 difference along the frequency spectrum between models is observed, see
Fig. 4.29. The real case, on the other hand, may present some phenomena which are
not included in neither of the models. For instance, the models do not consider any
transverse wave or mode conversion. These may be present in the experiment, by
means of non-perpendicular path, due to the transducer beam divergence, and the
converted modes of indirect incidence.
105
The system showed itself to be able to communicate with the sensor by
amplitude modulating the carrier signal, generated in the “outside block”, varying
the electrical impedance load of the “inside” transducer. Specifically, concerning
the curved wall-water configuration, in which the developed prototype were
applied, the achieved results showed that the system can communicate with the
sensor at a data rate of 9600 bps when interrogated once per second. The power
consumption of the “inside block” was calculated to be approximately 135mW,
which is well below the capacity of the channel, measured at 1.4W when setting the
output power at 10 W.
The last experiment compared the communication of a temperature sensor
through the acoustic channel with raw sensor data, directed connected to a computer
terminal. Communication was established successfully and the system kept running
for approximately four hours. There were two events when it did not operated
correctly and required manual intervention. It was caused mainly due to the high
frequency selectivity of the acoustic channel.
Lastly, one can conclude that the experiments conducted in the laboratory,
with a flat aluminum plate and curved carbon steel along with a water layer, has
shown feasibility to communicate and power an isolated circuitry, in the “inside
block”, that comprises a low-power microcontroller and digital pressure and
temperature sensor. Some identified that the system vulnerability when using wall-
water configuration is possibily due to coaxial misalignment. between emitter and
receiver transducers and acoustic velocities variation of the materials, which is
caused by the dependence of temperature, inducing a dramatically attenuation of
power and data communication capability.
Some points can be raised as future works. One can improve solutions for
data demodulation by eliminating the analog voltage comparator and implementing
the demodulation using digital signal processing techniques in microcontroller or a
digital signal processor (DSP), which would render the system less sensitivity to
noise. Additionally, dynamical tracking the optimum operating frequency avoids
the systems increase of package loss. techniques like genetic algorithm or neural
network may help predicting the best frequency to operate. Some other possible
future work could be:
106
• Studies regarding the cavitation-like phenomena to clarify the power
transfer when the transducer is in contact with fluids [98], since it
causes heat on the transducer and bubbles on the fluid with possibility
of degradation.
• Extension and developing of numerical and analytical models
focusing on the curved surface problem [96, 97] in order to understand
power and data transfer behavior.
• Studies on the dependence of temperature and pressure on the system,
mainly the adhesive material, since its acoustic properties starts
degrading due to temperature variation [91].
• Studies on the impact of misalignment between transducers both
circumferential as well as longitudinal.
• Studies on the acoustic reverberation in multiple layers and techniques
in order to focus the acoustic energy between transmitter and receiver
transducers [112].
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